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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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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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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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Perfect Matchings and Perfect Powers [PDF]
Journal of Algebraic Combinatorics, 2003 In the last decade there have been many results about special families of graphs whose number of perfect matchings is given by perfect or near perfect powers. In this paper we present an approach that allows proving them in a unified way. We use this approach to prove a conjecture of James Propp stating that the number of tilings of the so-called Aztec
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Neuroplasticity and MRI: A perfect match [PDF]
NeuroImage, 2016 Numerous studies have illustrated the benefits of physical workout and cognitive exercise on brain function and structure and, more importantly, on decelerating cognitive decline in old age and promoting functional rehabilitation following injury. Despite these behavioral observations, the exact mechanisms underlying these neuroplastic phenomena remain
Julie Hamaide +2 more
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Discrete Mathematics, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
James Haglund, Jeffrey B. Remmel
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Bichromatic Perfect Matchings with Crossings
, 2023 Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023)
Oswin Aichholzer +4 more
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