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Perfect Matchings with Crossings [PDF]
Algorithmica, 2022 Abstract For sets of n points, n even, in general position in the plane, we consider straight-line drawings of perfect matchings on them. It is well known that such sets admit at least
Oswin Aichholzer +7 more
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The Approximate Degree of Bipartite Perfect Matching [PDF]
, 2022 The approximate degree of a Boolean function is the least degree of a real multilinear polynomial approximating it in the _∞-norm over the Boolean hypercube.
Beniamini, Gal
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Families with no perfect matchings [PDF]
Combinatorial Theory, 2021 We consider families of $k$-subsets of $\{1, \dots, n\}$, where $n$ is a multiple of $k$, which have no perfect matching. An equivalent condition for a family $\mathcal{F}$ to have no perfect matching is for there to be a blocking set, which is a set of $b$ elements of $\{1, \dots, n\}$ that cannot be covered by $b$ disjoint sets in $\mathcal{F}$.
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Perfect Matching Preservers [PDF]
The Electronic Journal of Combinatorics, 2006 For two bipartite graphs $G$ and $G'$, a bijection $\psi: E(G) \rightarrow E(G')$ is called a (perfect) matching preserver provided that $M$ is a perfect matching in $G$ if and only if $\psi(M)$ is a perfect matching in $G'$. We characterize bipartite graphs $G$ and $G'$ which are related by a matching preserver and the matching preservers between them.
Richard A. Brualdi +2 more
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On perfect matchings in matching covered graphs [PDF]
Journal of Graph Theory, 2018 AbstractA graph is matching‐covered if every edge of is contained in a perfect matching. A matching‐covered graph is strongly coverable if, for any edge of , the subgraph is still matching‐covered. An edge subset of a matching‐covered graph is feasible if there exist two perfect matchings and such that , and an edge subset with at least two ...
Jinghua He +3 more
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Eigenvalues and perfect matchings [PDF]
Linear Algebra and its Applications, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Brouwer, A.E., Haemers, W.H.
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Markov Equilibria in Dynamic Matching and Bargaining Games [PDF]
, 2004 Rubinstein and Wolinsky (1990) show that a simple homogeneous market with exogenous matching has continuum of (non-competitive) perfect equilibria, but the unique Markov perfect equilibrium is competitive.
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Fractional matching preclusion for butterfly derived networks
Theory and Applications of Graphs, 2019 The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings.
Xia Wang +4 more
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Low Weight Perfect Matchings [PDF]
The Electronic Journal of Combinatorics, 2020 Answering a question posed by Caro, Hansberg, Lauri, and Zarb, we show that for every positive integer $n$ and every function $\sigma\colon E(K_{4n})\to\{-1,1\}$ with $\sigma\left(E(K_{4n})\right)=0$, there is a perfect matching $M$ in $K_{4n}$with $\sigma(M)=0$.
Stefan Ehard +2 more
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Planar cycle-extendable graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceFor most problems pertaining to perfect matchings, one may restrict attention to matching covered graphs - that is, connected nontrivial graphs with the property that each edge belongs to some perfect matching.
Aditya Y Dalwadi +3 more
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