Academic literature on the topic 'Perfect matching polytope'
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Journal articles on the topic "Perfect matching polytope":
WANG, XIUMEI, WEIPING SHANG, YIXUN LIN, and MARCELO H. CARVALHO. "A CHARACTERIZATION OF PM-COMPACT CLAW-FREE CUBIC GRAPHS." Discrete Mathematics, Algorithms and Applications 06, no. 02 (March 19, 2014): 1450025. http://dx.doi.org/10.1142/s1793830914500256.
de Carvalho, Marcelo H., Cláudio L. Lucchesi, and U. S. R. Murty. "The perfect matching polytope and solid bricks." Journal of Combinatorial Theory, Series B 92, no. 2 (November 2004): 319–24. http://dx.doi.org/10.1016/j.jctb.2004.08.003.
Lin, Ruizhi, and Heping Zhang. "Fractional matching preclusion number of graphs and the perfect matching polytope." Journal of Combinatorial Optimization 39, no. 3 (January 29, 2020): 915–32. http://dx.doi.org/10.1007/s10878-020-00530-2.
Rispoli, Fred J. "The Monotonic Diameter of the Perfect 2-matching Polytope." SIAM Journal on Optimization 4, no. 3 (August 1994): 455–60. http://dx.doi.org/10.1137/0804025.
Bian, Hong, and Fuji Zhang. "The graph of perfect matching polytope and an extreme problem." Discrete Mathematics 309, no. 16 (August 2009): 5017–23. http://dx.doi.org/10.1016/j.disc.2009.03.009.
Lin, Yixun, and Xiumei Wang. "Core index of perfect matching polytope for a 2-connected cubic graph." Discussiones Mathematicae Graph Theory 38, no. 1 (2018): 189. http://dx.doi.org/10.7151/dmgt.2001.
Behrend, Roger E. "Fractional perfect b -matching polytopes I: General theory." Linear Algebra and its Applications 439, no. 12 (December 2013): 3822–58. http://dx.doi.org/10.1016/j.laa.2013.10.001.
Wang, Xiumei, and Yixun Lin. "Three-matching intersection conjecture for perfect matching polytopes of small dimensions." Theoretical Computer Science 482 (April 2013): 111–14. http://dx.doi.org/10.1016/j.tcs.2013.02.023.
Rispoli, Fred J. "The monotonic diameter of the perfect matching and shortest path polytopes." Operations Research Letters 12, no. 1 (July 1992): 23–27. http://dx.doi.org/10.1016/0167-6377(92)90018-x.
Atserias, Albert, Anuj Dawar, and Joanna Ochremiak. "On the Power of Symmetric Linear Programs." Journal of the ACM 68, no. 4 (July 28, 2021): 1–35. http://dx.doi.org/10.1145/3456297.
Dissertations / Theses on the topic "Perfect matching polytope":
Pisanu, Francesco. "On box-total dual integrality and total equimodularity." Electronic Thesis or Diss., Paris 13, 2023. http://www.theses.fr/2023PA131044.
In this thesis, we study box-totally dual integral (box-TDI) polyhedra associated with severalproblems and totally equimodular matrices. Moreover, we study the complexity of some funda-mental questions related to them.We start by considering totally equimodular matrices, which are matrices such that, forevery subset of linearly independent rows, all nonsingular maximal submatrices have the samedeterminant in absolute value. Despite their similarities with totally unimodular matrices, wehighlight several differences, even in the case of incidence and adjacency matrices of graphs.As is well-known, the incidence matrix of a given graph is totally unimodular if and only if thegraph is bipartite. However, the total equimodularity of an incidence matrix depends on whetherwe consider the vertex-edge or the edge-vertex representation. We provide characterizations forboth cases. As a consequence, we prove that recognizing whether a given polyhedron is box-TDIis a co-NP-complete problem.Characterizing the total unimodularity or total equimodularity of the adjacency matrix of agiven bipartite graph remains unsolved, while we solved the corresponding problem in the case oftotal equimodularity when the graph is nonbipartite.In a later part of this work, we characterize the graphs for which the perfect matching polytope(PMP) is described by trivial inequalities and the inequalities corresponding to tight cuts. Tightcuts are defined as cuts that share precisely one edge with each perfect matching. We thenprove that any graph for which the corresponding PMP is box-TDI belongs to this class. Asa consequence, it turns out that recognizing whether the PMP is box-TDI is a polynomial-timeproblem. However, we provide several counterexamples showing that this class of graphs does notguarantee the box-TDIness of the PMP.Lastly, we present necessary conditions for the box-TDIness of the edge cover polytope andcharacterize the box-TDIness of the extendable matching polytope, which is the convex hull ofthe matchings included in a perfect matching
Book chapters on the topic "Perfect matching polytope":
Lucchesi, Cláudio L., and U. S. R. Murty. "The Perfect Matching Polytope." In Perfect Matchings, 111–37. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-47504-7_6.
Cardinal, Jean, and Raphael Steiner. "Inapproximability of Shortest Paths on Perfect Matching Polytopes." In Integer Programming and Combinatorial Optimization, 72–86. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-32726-1_6.