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A Generalized Matching Reconfiguration Problem [article]

Noam Solomon, Shay Solomon
<span title="2020-05-05">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The running time of these procedures is linear. We further demonstrate the applicability of this generalized problem to dynamic graph matchings.  ...  In the Matching Reconfiguration Problem (MRP), proposed in a pioneering work by Ito et al. from 2008, we are given a graph G and two matchings M and M', and we are asked whether there is a sequence of  ...  It is easy to see that this stability property generalizes for weighted matchings, where the maximum matching weight may change by an additive factor of at most ψ.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1803.05825v3">arXiv:1803.05825v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u5yvmwph45etza7wpjeob6imea">fatcat:u5yvmwph45etza7wpjeob6imea</a> </span>
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Strong f-star factors of graphs

Zheng Yan
<span title="">2015</span> <i title="Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Gora"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g64zvtslcjdqncvrfbmvf422qi" style="color: black;">Discussiones Mathematicae Graph Theory</a> </i> &nbsp;
Let G be a graph and  ...  Mikio Kano for introducing me to problems on factors of graph and for his valuable suggestions.  ...  A formula for the order of a maximum strong f -star subgraph of a graph is easily obtained as a maximum matching, which is given in the following theorem. Theorem 6.  ... 
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The matching relaxation for a class of generalized set partitioning problems [article]

Phillippe Samer, Evellyn Cavalcante, Sebastián Urrutia, Johan Oppen
<span title="2018-05-11">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show how that general method can be tailored to sample applications, and also perform a successful computational evaluation with benchmark instances of a problem in maritime logistics.  ...  We present two combinatorial relaxations based on computing maximum weighted matchings in suitable graphs.  ...  Finally, it could be interesting to study alternative relaxations of the base GSPP structure, e.g. comparing combinatorial and Lagrangean bounds, or even extending the relax-and-cut approach of Cavalcante  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1606.09279v5">arXiv:1606.09279v5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wz2n7mwv3rf7zbwzoplsg3h7gq">fatcat:wz2n7mwv3rf7zbwzoplsg3h7gq</a> </span>
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f-Factors and related decompositions of graphs

J.E Graver, W.B Jurkat
<span title="">1980</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g6u5fful5vcr3a7gppc6y47el4" style="color: black;">Journal of combinatorial theory. Series B (Print)</a> </i> &nbsp;
In general it is desirable to find decompositions of a graph so that the factor problem for the whole graph can be solved through corresponding problems for the various parts.  ...  Hence, by (1.3) again, G has an f-matching iff A(G, f) = f(B)f(A). ( 2 2 -l) Thus the value of A(G, f) decides upon the existence of f-factors and f-matchings.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0095-8956(80)90056-8">doi:10.1016/0095-8956(80)90056-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2hoomq3qwngolgrcnhynxp7yi4">fatcat:2hoomq3qwngolgrcnhynxp7yi4</a> </span>
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Maximum (g,f)-factors of a general graph

William Y.C. Chen
<span title="">1991</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
., Maximum (g, f)-factors of a general graph, Discrete Mathematics 91 (1991) l-7. 0012-365X/91/$03.50 0 1991-Elsevier Science Publishers B.V. (North-Holland)  ...  Oliveira for their valuable suggestions, and to thank A. Shastri for helpful discussions about an early version of this paper.  ...  In this paper, we shall consider the problem of characterizing maximum (g,f)-factors of G if G contains (g, f)-factors.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(91)90158-x">doi:10.1016/0012-365x(91)90158-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vczmfzadb5dp5gnkk2xeeuwkba">fatcat:vczmfzadb5dp5gnkk2xeeuwkba</a> </span>
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Characterizations of maximum fractional (g,f)-factors of graphs

Guizhen Liu, Lanju Zhang
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
In this paper a characterization of maximum fractional (g, f )-factors of a graph is presented.  ...  Chen, Maximum (g, f )-factors of a general graph, Discrete Math. 91 (1991) 1-7] and [Edward R. Scheinerman, Daniel H. Ullman, Fractional Graph Theory, John Wiley and Sonc, Inc., New York, 1997].  ...  Acknowledgments The authors are indebted to the anonymous referees for pointing out a gap in the proof of Theorem 2.1, and valuable comments and suggestions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2007.10.016">doi:10.1016/j.dam.2007.10.016</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/63kf5ugwu5g5benjkiihqnwkey">fatcat:63kf5ugwu5g5benjkiihqnwkey</a> </span>
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A Note on the Existence of All (g,f)-Factors

Radosław Cymer
<span title="">2017</span> <i title="Journal of Graph Algorithms and Applications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4joumle7hffilk276fkubvhxcq" style="color: black;">Journal of Graph Algorithms and Applications</a> </i> &nbsp;
This paper is devoted to the problem of existence of all (g, f )-factors in a bipartite graph. We present an algorithm to test if a given bipartite graph contains all (g, f )-factors.  ...  An analogous result for general graphs remains still unanswered.  ...  This means that the open problem of efficiently checking whether a graph has all (g, f )-factors still remains not solved for general case. and g(x 3 ) = 2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7155/jgaa.00429">doi:10.7155/jgaa.00429</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jv3xmpctizbwzal7lkqzxrkmla">fatcat:jv3xmpctizbwzal7lkqzxrkmla</a> </span>
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Minconvex graph factors of prescribed size and a simpler reduction to weighted f-factors

Annabell Berger, Winfried Hochstättler
<span title="">2007</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fhi2xwpnh5gmlgof2idwu5wlgq" style="color: black;">Electronic Notes in Discrete Mathematics</a> </i> &nbsp;
Alternating walks If is the sum of squares of the degrees and G has a matching M ⊆ E of size k then clearly M is optimal for Problem 2.2 which, thus, generalizes matching (see e.g. [4] ).  ...  More generally, they examine the problem to find F ⊆ E in a given, not necessarily simple, graph G = (V, E), such that |F | = k and (d F ) := v∈V v (d F (v)) is minimized, where is a discrete separable  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.endm.2007.01.011">doi:10.1016/j.endm.2007.01.011</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/t24whpeg75fmjnuwnkg2qasjji">fatcat:t24whpeg75fmjnuwnkg2qasjji</a> </span>
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A note on the f-factor-lattice of bipartite graphs

J Rieder
<span title="">1992</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g6u5fful5vcr3a7gppc6y47el4" style="color: black;">Journal of combinatorial theory. Series B (Print)</a> </i> &nbsp;
GENERALIZATIONS The f-factors of G can be regarded as a graphic representation of the common bases of two general partition matroids.  ...  In the case off -1 Y(G, f) is the family of the perfect matchings of G. (For an introduction to graph theory see, e.g., [ 11.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0095-8956(92)90009-m">doi:10.1016/0095-8956(92)90009-m</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ckkdhgji5vbxdkskv7ae727rgu">fatcat:ckkdhgji5vbxdkskv7ae727rgu</a> </span>
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On the Complexity Landscape of Connected f -Factor Problems [article]

R. Ganian, N. S. Narayanaswamy, S. Ordyniak, C. S. Rahul, M. S. Ramanujan
<span title="2018-12-05">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A classical result of Tutte(1954) is the polynomial time algorithm to check whether a given graph has a specified f-factor.  ...  However, checking for the presence of a connected f-factor is easily seen to generalize HAMILTONIAN CYCLE and hence is NP-complete.  ...  Unlike the general f -factor problem, deciding the existence of a connected f -factor is NPcomplete [6, 2] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1812.02037v1">arXiv:1812.02037v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jmcoigufmrc45ebv64lnnfzx4q">fatcat:jmcoigufmrc45ebv64lnnfzx4q</a> </span>
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On the Complexity Landscape of Connected f-Factor Problems

R. Ganian, N. S. Narayanaswamy, S. Ordyniak, C. S. Rahul, M. S. Ramanujan
<span title="2019-01-30">2019</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qhi3z76be5c5xeihac5cyiid3m" style="color: black;">Algorithmica</a> </i> &nbsp;
Lemma 38 For every c > 1 and for every g(n) ∈ Θ((log n) c ), CONNECTED g-BOUNDED f -FACTOR is not NP-hard unless the Exponential Time Hypothesis fails. Acknowledgments.  ...  We first show that the problem is not NP-hard unless the ETH fails.  ...  Lemma 26 ([22]) A graph G has an f -factor if and only if the f -blowup of G has a perfect matching.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00453-019-00546-z">doi:10.1007/s00453-019-00546-z</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gp62r3kx2bfyfa7hokjfoxvsbi">fatcat:gp62r3kx2bfyfa7hokjfoxvsbi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210427091516/http://eprints.whiterose.ac.uk/167897/1/journal-factor.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/5e/59/5e5920e1cea971ad8effc619234ac0536a4dc76a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00453-019-00546-z"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

A Weight-scaling Algorithm for f-factors of Multigraphs [article]

Harold Gabow
<span title="2020-10-02">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The algorithm is a direct generalization of the algorithm of Gabow and Tarjan for the special case of ordinary matching (f≡ 1).  ...  A recent algorithm of Duan and He et al. for f-factors of simple graphs comes within logarithmic factors of this bound, O (n^2/3 m log W).  ...  We resolve the problem of ineligible base edges in a general fashion, that may find other applications.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2010.01102v1">arXiv:2010.01102v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/brinujdbwregpmhniryiy5yfby">fatcat:brinujdbwregpmhniryiy5yfby</a> </span>
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A combinatoric interpretation of dual variables for weighted matching and f-factors

Harold N. Gabow
<span title="">2012</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 all cases the y duals are canonical in a well-defined sense; z duals are canonical for matching and more generally for b-matchings (a special case of f -factors) but for f -factors their support can  ...  Of course we show the same extension to maximum weight perfect matching and f -factors. For general graph f -factors the same description of the duals applies, 1 using 2f -unifactors.  ...  Acknowledgments I thank the referee for a thorough and insightful report that substantively improved this paper, and also for reminding me about references on algebraic matching.  ... 
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A Characterization for the Existence of Connected f-Factors of Large Minimum Degree [article]

N S Narayanaswamy, C S Rahul
<span title="2016-01-23">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present a diameter based characterization of graphs having a connected f-factor (for such f).  ...  We show that if a graph G has a connected f-factor and an f-factor with 2 connected components, then it has a connected f-factor of diameter at least 3.  ...  This result can be seen as a generalization of the Tutte's reduction of the f -factor problem to the graph perfect matching problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1601.06291v1">arXiv:1601.06291v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2pspgqpa5rdndm6e3u5c3kgote">fatcat:2pspgqpa5rdndm6e3u5c3kgote</a> </span>
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Packing bipartite graphs with covers of complete bipartite graphs

Jérémie Chalopin, Daniël Paulusma
<span title="">2014</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
For a set S of graphs, a perfect S-packing (S-factor) of a graph G is a set of mutually vertex-disjoint subgraphs of G that each are isomorphic to a member of S and that together contain all vertices of  ...  We settle the computational complexity of the problem that asks whether a graph allows a pseudo-covering to K k, for all fixed k, ≥ 1.  ...  We thank the two anonymous referees for useful comments that helped us to improve the readability of our paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2012.08.026">doi:10.1016/j.dam.2012.08.026</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6ku6d6cqu5gj5cpbq67lie4vj4">fatcat:6ku6d6cqu5gj5cpbq67lie4vj4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170705081624/http://pageperso.lif.univ-mrs.fr/~jeremie.chalopin/publis/CP-DAM12.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/03/db/03dbbd34f01935cd881c967a27fc4f597c68ed6e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2012.08.026"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> elsevier.com </button> </a>
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