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The subgraph homeomorphism problem on reducible flow graphs [chapter]

T. Hirata, M. Kimura
<span title="">1981</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 the subgraph homeomorphism problem in which one would like to determine whether a fixed pattern graph is hcmeomorphic to a subgraph of an input graph.  ...  We show that for every fixed pattern graph, there is a polynomial-time algorithm to solve the problem if the input graphs are restricted to reducible flow graphs.  ...  Nishizeki for his careful reading of the manuscript and valuable comments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-10704-5_7">doi:10.1007/3-540-10704-5_7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zc24jugo3ja77kyf7sj6ktgm3u">fatcat:zc24jugo3ja77kyf7sj6ktgm3u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180728202538/https://link.springer.com/content/pdf/10.1007%2F3-540-10704-5_7.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/99/ac/99acd2f2683984a1e921d580b3b8ac176c5fbce9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-10704-5_7"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

The directed subgraph homeomorphism problem

Steven Fortune, John Hopcroft, James Wyllie
<span title="">1980</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 set of pattern graphs for which the fixed directed subgraph homeomorphism problem is NP-complete is characterized. A polynomial time algorithm is given for the remaining cases.  ...  The restricted problem where the input graph is a directed acyclic graph is in polynomial ti. ie for all pattern graphs and an algorithm is giver?. *  ...  Other applications of scbgraph homeomorphism include flow graph reducibility [3] and programming schema [41] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(80)90009-2">doi:10.1016/0304-3975(80)90009-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7apefd3sy5adfg3jiosfirln4y">fatcat:7apefd3sy5adfg3jiosfirln4y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170924113329/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/140/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMzA0Mzk3NTgwOTAwMDky.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/a8/b4/a8b4454807b8993755817903f19a7f1b3751a34a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(80)90009-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

The subgraph homeomorphism problem

Andrea S. LaPaugh, Ronald L. Rivest
<span title="">1978</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jlc5kugafjg4dl7ozagimqfcbm" style="color: black;">Proceedings of the tenth annual ACM symposium on Theory of computing - STOC &#39;78</a> </i> &nbsp;
The most general subgraph homeomorphism problem-given as input graphs G and H, is H homeomorphic to a subgraph ,of G ?  ...  The pattern graph His homeomorphic to a subgraph of G if and only if H' is homeomorphic to a subgraph of one of the graphs in the set So .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/800133.804330">doi:10.1145/800133.804330</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/stoc/LapaughR78.html">dblp:conf/stoc/LapaughR78</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/t56qeq5v3zbjxizho4h22xbkpa">fatcat:t56qeq5v3zbjxizho4h22xbkpa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20130413030706/http://people.csail.mit.edu/rivest/pubs/LPR80.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/d6/4c/d64c8b4725b797b9bff9e3bf889476342bfe78ae.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/800133.804330"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

The subgraph homeomorphism problem

Andrea S. Lapaugh, Ronald L. Rivest
<span title="">1980</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6ovb2qpkfenhmb7mcksobrcxq" style="color: black;">Journal of computer and system sciences (Print)</a> </i> &nbsp;
The most general subgraph homeomorphism problem-given as input graphs G and H, is H homeomorphic to a subgraph ,of G ?  ...  The pattern graph His homeomorphic to a subgraph of G if and only if H' is homeomorphic to a subgraph of one of the graphs in the set So .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0022-0000(80)90057-4">doi:10.1016/0022-0000(80)90057-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o2atxpvhknhetehuvmburglw3q">fatcat:o2atxpvhknhetehuvmburglw3q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190416080941/https://core.ac.uk/download/pdf/82478537.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/c8/6f/c86f91a76d4aef0ca08e7e1b31fa4c943b3a74ec.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0022-0000(80)90057-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

A Polynomial-Time Algorithm for Detecting the Possibility of Braess Paradox in Directed Graphs

Pietro Cenciarelli, Daniele Gorla, Ivano Salvo
<span title="2018-07-23">2018</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qhi3z76be5c5xeihac5cyiid3m" style="color: black;">Algorithmica</a> </i> &nbsp;
The resulting algorithm also contributes to another well known problem, i.e. the directed subgraph homeomorphism problem without node mapping, by providing another pattern graph for which a polynomial  ...  In this paper, we give a graph-theoretic characterisation of vulnerable directed multigraphs; analogous results appeared in the literature only for undirected multigraphs and for a specific family of directed  ...  On the Directed Subgraph Homeomorphism Problem Theorem 4.4 and Algorithm 1 have consequences on another, long-standing problem: the directed subgraph homeomorphism [8] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00453-018-0486-6">doi:10.1007/s00453-018-0486-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hckjpq3qf5arvoc5b3e2vxgoq4">fatcat:hckjpq3qf5arvoc5b3e2vxgoq4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191019133816/https://arxiv.org/pdf/1610.09320v3.pdf" title="fulltext PDF download [not primary version]" 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] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1a/69/1a69ccc7827a2fbdfa5c34d2165e506f586336c5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00453-018-0486-6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

A minimization version of a directed subgraph homeomorphism problem

Janina A. Brenner, Sándor P. Fekete, Jan C. van der Veen
<span title="2008-09-20">2008</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2zozqedzyrg2bmn5ala6o7d5se" style="color: black;">Mathematical Methods of Operations Research</a> </i> &nbsp;
We consider a special case of the directed subgraph homeomorphism or topological minor problem, where the host graph has a specific regular structure.  ...  In this application domain, the task is to simultaneously schedule, bind and route a so-called data-flow graph, where vertices represent operations and arcs stand for data dependencies between the operations  ...  Due to the representation as a subgraph homeomorphism problem, we also speak of a solution to the SSBR problem as an embedding of the data-flow graph in the grid H .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00186-008-0259-0">doi:10.1007/s00186-008-0259-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/a4xcfeipxjhafc65ighdu62yxm">fatcat:a4xcfeipxjhafc65ighdu62yxm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190303145756/http://pdfs.semanticscholar.org/cb71/a4bd7193c251a8e22efbf02f450af28a0cd0.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/cb/71/cb71a4bd7193c251a8e22efbf02f450af28a0cd0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00186-008-0259-0"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Graph Minor Approach for Application Mapping on CGRAs

Liang Chen, Tulika Mitra
<span title="2014-09-03">2014</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qfvmhupy5fb6tcrtb2orjpq5e4" style="color: black;">ACM Transactions on Reconfigurable Technology and Systems</a> </i> &nbsp;
We formalize the CGRA mapping problem as a graph minor containment problem.  ...  We design an exact graph minor testing approach that exploits the unique properties of both the data flow graph and the routing resource graph to significantly prune the search space.  ...  We formalize the CGRA mapping problem as restricted graph minor containment of the data flow graph representing the computation kernel in the modulo routing resource graph representing the CGRA architecture  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2655242">doi:10.1145/2655242</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nitqwddh2jcwbng3qjdnf6nm34">fatcat:nitqwddh2jcwbng3qjdnf6nm34</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808235910/http://www.comp.nus.edu.sg/~tulika/TRB6-13.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/dd/cb/ddcb3750002deebe4804aa86d4c411f912cf865d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2655242"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Page 2224 of Mathematical Reviews Vol. , Issue 91D [page]

<span title="">1991</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The problems are the following: (1) Fixed subgraph ho- meomorphism: determine whether a graph contains a subgraph homeomorphic to a given graph. (2) The disjoint connecting path problem with bounded number  ...  problem, and the minimum cost flow problem.  ... 
<span class="external-identifiers"> </span>
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Topological classification of $Ω$-stable flows on surfaces by means of effectively distinguishable multigraphs

Vladislav Kruglov, Dmitry Malyshev, Olga Pochinka
<span title="">2018</span> <i title="American Institute of Mathematical Sciences (AIMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rcpeuakxozcbxkr5eegcbenv4q" style="color: black;">Discrete and Continuous Dynamical Systems. Series A</a> </i> &nbsp;
However, in the present paper we prove that a topological classification of such flows is also reduced to a combinatorial problem.  ...  The violation of the last property leads to Ω-stable flows on surfaces, which are not structurally stable.  ...  Nevertheless, it is possible to reduce the problem for four-colour graphs to the same problem for simple graphs with a small complexity of the reduction.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3934/dcds.2018188">doi:10.3934/dcds.2018188</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/c5ssj3dobbbb3pjktewytcz5ae">fatcat:c5ssj3dobbbb3pjktewytcz5ae</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200306132056/https://www.aimsciences.org/article/exportPdf?id=95661ed6-5dc1-478e-8466-21a937e2e13b" 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/72/fd/72fd6424ea78a2ac1abdcce435736e29a333a93e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3934/dcds.2018188"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Existence, uniqueness and monotonic behavior of the solution of classical flow distribution problem for hydraulic networks with pressure-dependent closure relations

Leonid Korelstein, N.N. Novitsky, B. Serttter, V.R. Chupin, E. Khaltar, L.B. Korelstein, S.A. Miedema, M. Negnevitsky, C. Sarica, F.H. Mirelli, V.A. Stennikov, M.G. Sukharev (+2 others)
<span title="">2019</span> <i title="EDP Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wehsdgmkgvabfewguumql7pepe" style="color: black;">E3S Web of Conferences</a> </i> &nbsp;
Existence, uniqueness and monotonic behavior of the solution of classical flow distribution problem for hydraulic networks with pressure-dependent closure relations was proved.  ...  The closure relation can have very general form, restricted only by continuity and monotonicity conditions necessary for providing existence, uniqueness and continuity of flow distribution problem for  ...  Graph ( ) cen be non-connected, let its connected subgraphs, and sungraphs, from which they are produced (see example on Fig.2 ). We will call -Pcomponents of graph , and its P-reduced components.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1051/e3sconf/201910201004">doi:10.1051/e3sconf/201910201004</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/aripx3h2avdmlnkhc337o3tpnu">fatcat:aripx3h2avdmlnkhc337o3tpnu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200214145403/https://www.e3s-conferences.org/articles/e3sconf/pdf/2019/28/e3sconf_mmmaosdphs18_01004.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/7f/2d/7f2d7559274ad6671ac01d9281d2225478d19174.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1051/e3sconf/201910201004"> <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>

Inefficiencies in network models: A graph-theoretic perspective

Pietro Cenciarelli, Daniele Gorla, Ivano Salvo
<span title="">2018</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5xfy4fcdxvcvdiybp6iqbffqc4" style="color: black;">Information Processing Letters</a> </i> &nbsp;
We then consider the standard flow networks with capacity on edges, where again efficiency is related to maximality of saturating flows, and a traffic model for selfish routing, where efficiency is related  ...  Finally, we show that all these forms of inefficiency yield different classes of graphs (apart from the acyclic case, where the last two forms generate the same class).  ...  Acknowledgements The authors wish to thank Irene Finocchi and Fabrizio Grandoni for helpful discussions about the topic of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ipl.2017.10.008">doi:10.1016/j.ipl.2017.10.008</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/viqpwqzhfrhy3fiw5q3rvdehxe">fatcat:viqpwqzhfrhy3fiw5q3rvdehxe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200831005000/https://arxiv.org/pdf/1603.01983v1.pdf" title="fulltext PDF download [not primary version]" 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] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/be/30/be30fda58412b3f9ad628710e65a6f80db790b8b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ipl.2017.10.008"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Minimum cuts and shortest homologous cycles

Erin W. Chambers, Jeff Erickson, Amir Nayyeri
<span title="">2009</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zqbrzpfj5rc3pcxpllbrit3n4q" style="color: black;">Proceedings of the 25th annual symposium on Computational geometry - SCG &#39;09</a> </i> &nbsp;
Except for the special case of planar graphs, for which O(n log n)-time algorithms have been known for more than 20 years, the best previous time bounds for finding minimum cuts in embedded graphs follow  ...  We describe the first algorithms to compute minimum cuts in surface-embedded graphs in near-linear time.  ...  The authors would like to thank Chandra Chekuri and Aparna Sundar for helpful discussions, and the anonymous reviewers for their comments and suggestions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1542362.1542426">doi:10.1145/1542362.1542426</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/compgeom/ChambersEN09.html">dblp:conf/compgeom/ChambersEN09</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/77bdajq6i5ax7cpbzwxek26bve">fatcat:77bdajq6i5ax7cpbzwxek26bve</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170813071746/http://cs.slu.edu/~chambers/papers/surfcut.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/68/a9/68a9900b764beb59f06f3c46a5dac5803790f321.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1542362.1542426"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

The combinatorics of gradient-like flows and foliations on closed surfaces: I. Topological classification

Leonid Plachta
<span title="">2003</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hp7o5f6pmrg57k2m46s4syavf4" style="color: black;">Topology and its Applications</a> </i> &nbsp;
In terms of rotation graphs we construct the complete topological invariants for gradient-like flows on closed surfaces.  ...  In terms of the so-called current graphs we also construct a complete topological invariant for Morse-Smale foliations without closed orbits on closed orientable surfaces.  ...  The author would like also to thank the organizers of the Euro-Workshop "Foliations: Geometry and Dynamics", Warsaw, 2000, May 29-June 9, for the hospitality.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0166-8641(02)00086-x">doi:10.1016/s0166-8641(02)00086-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/24pz5x5dirax7plj7ov3chlcpm">fatcat:24pz5x5dirax7plj7ov3chlcpm</a> </span>
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Spanning eularian subgraphs, the splitting Lemma, and Petersen's theorem

Herbert Fleischner
<span title="">1992</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
In this paper we show that a bridgeless graph without 2-valent vertices has a spanning eulerian subgraph without isolated vertices.  ...  This result is obtained by applying the Splitting Lemma and Petersen's Theorem. On the other hand, it can be viewed as a generalization of this famous theorem.  ...  The Splitting Lemma has proved to be a useful tool for proving many results and/or reducing unsolved problems to special classes of graphs. Here is another application of this lemma. Theorem.  ... 
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Page 2341 of Mathematical Reviews Vol. , Issue 2002D [page]

<span title="">2002</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
It is interesting that the problem is reduced to the problem on the existence of a Hamiltonian cycle in a cubic planar graph, which is known to be NP-complete (Garey, Johnson and Tarjan).  ...  Suppose the graph G is 2-cell embedded on the surface F. Two homeomorphisms of F are said to be equivalent if they induce the same action on G.  ... 
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