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Panconnectivity and edge-pancyclicity of faulty recursive circulant G(2m,4)

Jung-Heum Park
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
In this paper, we investigate a problem on embedding paths into recursive circulant G(2 m , 4) with faulty elements (vertices and/or edges) and show that each pair of vertices in recursive circulant G(  ...  The bound m − 3 on the number of acceptable faulty elements is the maximum possible.  ...  In the next section, we will present some basic properties of recursive circulant G(2 m , 4).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2007.10.016">doi:10.1016/j.tcs.2007.10.016</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5myzwl36urffjiqpxtv3imsaea">fatcat:5myzwl36urffjiqpxtv3imsaea</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190413053601/https://core.ac.uk/download/pdf/82049104.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ad/2a/ad2ad5ea080dd3008ae619e953c74b8f5c8dab92.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2007.10.016"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Disjoint path covers in recursive circulants G(2m,4) with faulty elements

Sook-Yeon Kim, Jae-Ha Lee, Jung-Heum Park
<span title="">2011</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
In this paper, we analyze the k-disjoint path cover of recursive circulant G(2 m , 4) under the condition that at most f faulty vertices and/or edges are removed.  ...  A k-disjoint path cover of a graph is defined as a set of k internally vertex-disjoint paths connecting given sources and sinks in such a way that every vertex of the graph is covered by a path in the  ...  The recursive circulant G(N, d) has a recursive structure when N = cd m , 1 ≤ c < d [23] , based upon the following property. Property 1 ([23]).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2011.04.045">doi:10.1016/j.tcs.2011.04.045</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/izib7erpfneb7hq3bgpfcxsm4a">fatcat:izib7erpfneb7hq3bgpfcxsm4a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190412062721/https://core.ac.uk/download/pdf/82794984.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/95/96/9596f7cb3ad23abb3145bb207fd8a63053851f9b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2011.04.045"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

A family of Hamiltonian and Hamiltonian connected graphs with fault tolerance

Y-Chuang Chen, Yong-Zen Huang, Lih-Hsing Hsu, Jimmy J. M. Tan
<span title="2009-07-10">2009</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qhbautqnvzgwvm3vvdvieylhwq" style="color: black;">Journal of Supercomputing</a> </i> &nbsp;
Processor (vertex) faults and link (edge) faults may happen when a network is used, and it is meaningful to consider networks (graphs) with faulty processors and/or links.  ...  Therefore, some of the generalized hypercubes, twistedcubes, crossed-cubes, and Möbius cubes are optimal fault-tolerant Hamiltonian and optimal fault-tolerant Hamiltonian connected.  ...  Acknowledgements The authors would like to express their gratitude to the anonymous referees for their kind suggestions and useful comments on the original manuscript, which have greatly improved the quality of  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11227-009-0316-3">doi:10.1007/s11227-009-0316-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/v7gblgakcnc6xlu4gt4rgwglvq">fatcat:v7gblgakcnc6xlu4gt4rgwglvq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170814014356/https://ir.nctu.edu.tw/bitstream/11536/31997/1/000282225700005.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/28/0d/280dd5a78d11f153cced5793136870c1a05d058d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11227-009-0316-3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Many-to-many disjoint path covers in hypercube-like interconnection networks with faulty elements

Jung-Heum Park, Hee-Chul Kim, Hyeong-Seok Lim
<span title="">2006</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ll6bfs5o6bahfinh3u5z2cnyoy" style="color: black;">IEEE Transactions on Parallel and Distributed Systems</a> </i> &nbsp;
We apply our main results to recursive circulant G(2 m , 4) and a subclass of hypercubelike interconnection networks, called restricted HL-graphs.  ...  We apply our main results to recursive circulant G(2 m , 4) and a subclass of hypercube-like interconnection networks, called restricted HL-graphs.  ...  When N = 2 m and d = 4, recursive circulant G(2 m , 4) is an m-regular graph with 2 m vertices.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tpds.2006.37">doi:10.1109/tpds.2006.37</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/r3riu2oan5edbli7gf47446xvm">fatcat:r3riu2oan5edbli7gf47446xvm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170830044918/http://tcs.catholic.ac.kr/~jhpark/papers/many-to-many_DPC_in_HLG.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/94/43/94431473e3b12e42a82124a77a92201128286ae3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tpds.2006.37"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Fault-Hamiltonicity of Product Graph of Path and Cycle [chapter]

Jung-Heum Park, Hee-Chul Kim
<span title="">2003</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We investigate hamiltonian properties of Pm × Cn, m ≥ 2 and even n ≥ 4, which is bipartite, in the presence of faulty vertices and/or edges.  ...  A sufficient condition is derived for the graph with two faulty edges to have a hamiltonian cycle.  ...  Hamiltonian properties of P m × C n with faulty elements play an important role in discovering fault-hamiltonicity of such interconnection graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45071-8_33">doi:10.1007/3-540-45071-8_33</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jufyle6fkvecfhy63xfl3bjktu">fatcat:jufyle6fkvecfhy63xfl3bjktu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809032938/http://tcs.catholic.ac.kr/~jhpark/papers/fault_hamiltonicity_of_PmCn.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ba/91/ba9111ed9b43ea634787d71ffb8eed1b3e43e87b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45071-8_33"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Panconnectivity and pancyclicity of hypercube-like interconnection networks with faulty elements

Jung-Heum Park, Hyeong-Seok Lim, Hee-Chul Kim
<span title="">2007</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
path in G\F of every length from 2m − 3 to |V (G\F)| − 1 for any set F of faulty elements (vertices and/or edges) with |F| ≤ m − 3, and there exists a cycle of every length from 4 to |V (G\F)| for any  ...  Applying our results to a class of hypercube-like interconnection networks called restricted HL-graphs, we show that in a restricted HL-graph G of degree m (≥ 3), each pair of vertices are joined by a  ...  Recursive circulant G(2 m , 4) of degree m was shown to be 0-fault almost pancyclic in [2] and then m − 2-fault almost pancyclic in [20] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2007.02.029">doi:10.1016/j.tcs.2007.02.029</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/axbefevrvrdodblnmr6x3wmfeq">fatcat:axbefevrvrdodblnmr6x3wmfeq</a> </span>
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Panconnectivity and Pancyclicity of Hypercube-Like Interconnection Networks with Faulty Elements [chapter]

Jung-Heum Park, Hyeong-Seok Lim, Hee-Chul Kim
<span title="">2006</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
path in G\F of every length from 2m − 3 to |V (G\F)| − 1 for any set F of faulty elements (vertices and/or edges) with |F| ≤ m − 3, and there exists a cycle of every length from 4 to |V (G\F)| for any  ...  Applying our results to a class of hypercube-like interconnection networks called restricted HL-graphs, we show that in a restricted HL-graph G of degree m (≥ 3), each pair of vertices are joined by a  ...  Recursive circulant G(2 m , 4) of degree m was shown to be 0-fault almost pancyclic in [2] and then m − 2-fault almost pancyclic in [20] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11942634_31">doi:10.1007/11942634_31</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wmq7zq5cb5hcrjny26i27hwph4">fatcat:wmq7zq5cb5hcrjny26i27hwph4</a> </span>
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Hamiltonian properties on a class of circulant interconnection networks

Milan Basic
<span title="">2018</span> <i title="National Library of Serbia"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5h57vchldreh5kwnkzol2rss4m" style="color: black;">Filomat</a> </i> &nbsp;
It has been noticed that unitary Cayley graphs as a class of circulant graphs possess many good properties such as small diameter, mirror symmetry, recursive structure, regularity, etc. and therefore can  ...  While retaining the attractive properties of hypercubes such as node-symmetry, recursive structure, connectivity etc., these graphs achieve noticeable improvements in diameter [18] and possess a complete  ...  Concluding Remarks We propose the class of unitary Cayley graphs as a subclass of circulant graphs for efficient interconnection networks, since they possess many good properties such as small diameter  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2298/fil1801071b">doi:10.2298/fil1801071b</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rcgd2qmvxfh35hlspfzv46zswi">fatcat:rcgd2qmvxfh35hlspfzv46zswi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200313025215/http://www.doiserbia.nb.rs/img/doi/0354-5180/2018/0354-51801801071B.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/76/9c/769cd6358d012cc938ce8c912edb0f1e8faba276.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2298/fil1801071b"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

A recursively construction scheme for super fault-tolerant hamiltonian graphs

Y-Chuang Chen, Lih-Hsing Hsu, Jimmy J.M. Tan
<span title="">2006</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xkk23xlywfez5l246cnmlit4qq" style="color: black;">Applied Mathematics and Computation</a> </i> &nbsp;
Along the way, the recursive circulant graph is a special case of our construction scheme, and the super fault-tolerant hamiltonian property of recursive circulant graph is obtained.  ...  The aim of this paper is to investigate a construction scheme to construct various super fault-tolerant hamiltonian graphs.  ...  The recursive circulant graphs can be recursively constructed using our construction schemes. And therefore, they are in fact a subclass of our proposed family of graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.amc.2005.11.023">doi:10.1016/j.amc.2005.11.023</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3jsc5ize7nedboem7qdh3lm4se">fatcat:3jsc5ize7nedboem7qdh3lm4se</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170813003405/https://ir.nctu.edu.tw/bitstream/11536/12148/1/000239135700002.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/60/27/6027f2ed1db1f57fc085430e7b435f5bc20fd213.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.amc.2005.11.023"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Many-to-Many Disjoint Path Covers in a Graph with Faulty Elements [chapter]

Jung-Heum Park, Hee-Chul Kim, Hyeong-Seok Lim
<span title="">2004</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Applying our main result to interconnection graphs, we observe that when there are f or less faulty elements, all of recursive circulant G(2 m , 4), twisted cube T Qm, and crossed cube CQ m of degree m  ...  For a graph G to be f -fault hamiltonian (resp. f -fault hamiltonian-connected), it is necessary To a graph G with a set of faulty elements F , the definition of a manyto-many disjoint path cover can be  ...  By applying the above two theorems to interconnection graphs, we will show that all of recursive circulant G(2 m , 4), twisted cube T Q m , and crossed cube CQ m of degree m are f -fault many-to-many k-disjoint  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-30551-4_64">doi:10.1007/978-3-540-30551-4_64</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qkj7bz6uavbi7ijqzfivzzmphu">fatcat:qkj7bz6uavbi7ijqzfivzzmphu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170830044927/http://tcs.catholic.ac.kr/~jhpark/papers/many-to-many_DPC.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7a/b5/7ab55c3caf5043fdb3cd0aca303c959852b053ed.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-30551-4_64"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Fault Hamiltonicity of Meshes with Two Wraparound Edges [chapter]

Kyoung-Wook Park, Hyeong-Seok Lim, Jung-Heum Park, Hee-Chul Kim
<span title="">2004</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
As an application of fault-hamiltonicity of M2(m, n), we show that the n-dimensional hypercube is strongly hamiltonian laceable if there are at most n − 2 faulty elements and at most one faulty vertex.  ...  M 2 (m, n) is a spanning subgraph of P m × Cn which has interesting fault hamiltonian properties. We show that M 2 (m, n) with odd n is hamiltonian-connected and 1-fault hamiltonian.  ...  We consider the hamiltonian properties of a graph in the presence of faulty elements(vertices and/or edges).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-27798-9_44">doi:10.1007/978-3-540-27798-9_44</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lrmkq4pg7vadxgb2z4jkgdpc5a">fatcat:lrmkq4pg7vadxgb2z4jkgdpc5a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809032911/http://tcs.catholic.ac.kr/%7Ejhpark/papers/meshes_with_wraparound_edges.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/49/e7/49e7fac59dd8628839acb06af79d86577e365343.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-27798-9_44"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Fractional matching preclusion of fault Hamiltonian graphs [article]

Huiqing Liu, Shunzhe Zhang, Xinyuan Zhang
<span title="2020-04-28">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A graph G is said to be f-fault Hamiltonian if there exists a Hamiltonian cycle in G-F for any set F of vertices and/or edges with |F|≤ f.  ...  In this paper, we establish the FMP number and FSMP number of (δ-2)-fault Hamiltonian graphs with minimum degree δ≥ 3.  ...  Then α(G(d n , d)) ≤ d n −d n−1 2 for n ≥ 2 and d ≥ 3.Tsai et al. [32] researched Hamiltonian properties of faulty recursive circulant graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2001.03713v2">arXiv:2001.03713v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xu2sreae7reppeq63foj3zxjkq">fatcat:xu2sreae7reppeq63foj3zxjkq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200503114428/https://arxiv.org/pdf/2001.03713v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2001.03713v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Many-to-many two-disjoint path covers in restricted hypercube-like graphs

Sook-Yeon Kim, Jung-Heum Park
<span title="">2014</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
A Disjoint Path Cover (DPC for short) of a graph is a set of pairwise (internally) disjoint paths that altogether cover every vertex of the graph.  ...  In this paper, we show that every m-dimensional restricted hypercube-like graph with at most m − 3 faulty vertices and/or edges being removed has a paired (and unpaired) 2-DPC joining arbitrary two sources  ...  Note that every odd-dimensional recursive circulant G(2 m , 4) is included in RHL graphs (while not every evendimensional recursive circulant is).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2014.02.014">doi:10.1016/j.tcs.2014.02.014</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/m367arwmzvcormvwpotqan7iou">fatcat:m367arwmzvcormvwpotqan7iou</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170812122438/http://tcs.catholic.ac.kr/~jhpark/papers/paired_2-DPC_in_RHL.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/49/9d/499d9683478534e2fdfde99c29997bd0435103d4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2014.02.014"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Conditional matching preclusion for hypercube-like interconnection networks

Jung-Heum Park, Sang Hyuk Son
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
The conditional matching preclusion number of a graph with n vertices is the minimum number of edges whose deletion results in a graph without an isolated vertex that does not have a perfect matching if  ...  We develop some general properties on conditional matching preclusion and then analyze the conditional matching preclusion numbers for some HL-graphs, hypercube-like interconnection networks.  ...  We begin with a hamiltonian property of G(8, 4) with a single faulty edge, which will be utilized later. Proof. The proof is by an immediate inspection.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2009.02.041">doi:10.1016/j.tcs.2009.02.041</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qubqlwcoenehhezea6acsda3b4">fatcat:qubqlwcoenehhezea6acsda3b4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809032857/http://tcs.catholic.ac.kr/~jhpark/papers/ConditionalMatchingPreclusion.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/22/c8/22c824e90595a603390e6a7e8070da5f8c575a88.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2009.02.041"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

On the construction of paired many-to-many disjoint path covers in hypercube-like interconnection networks with faulty elements

Jung-Heum Park, Hee-Chul Kim, Hyeong-Seok Lim
<span title="">2008</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5vsih2yegrfubf7el6ncng3mgq" style="color: black;">Proceedings, International Parallel and Distributed Processing Symposium (IPDPS)</a> </i> &nbsp;
We show that every restricted HL-graph of degree m with f or less faulty elements has a paired many-to-many k-DPC for any f and k ≥ 2 with f + 2k ≤ m.  ...  A paired many-to-many k-disjoint path cover (k-DPC) of a graph G is a set of k disjoint paths joining k distinct source-sink pairs in which each vertex of G is covered by a path.  ...  are restricted HL-graphs with the exception of recursive circulant G(2 m , 4) and "near" bipartite interconnection networks such as twisted m-cube.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ipdps.2008.4536124">doi:10.1109/ipdps.2008.4536124</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/ipps/ParkKL08.html">dblp:conf/ipps/ParkKL08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wrhje6dgkbf6fd65xpwbz26slu">fatcat:wrhje6dgkbf6fd65xpwbz26slu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809032914/http://tcs.catholic.ac.kr/~jhpark/papers/paired_many-to-many_DPC_in_RHL.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/4e/53/4e53ca1d4757bfd17bbe63d3372ec478c529b0e3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ipdps.2008.4536124"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>
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