Results 21 to 30 of about 152,220 (203)
On characterizing proper max-point-tolerance graphs
AKCE International Journal of Graphs and Combinatorics, 2023 Max-point-tolerance graphs (MPTG) were introduced by Catanzaro et al. in 2017 as a generalization of interval graphs. This graph class has many practical applications in the study of the human genome as well as in signal processing for networks. The same
Sanchita Paul
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Perfect t-Embeddings of Uniformly Weighted Aztec Diamonds and Tower Graphs [PDF]
International mathematics research notices, 2023 In this work we study a sequence of perfect t-embeddings of uniformly weighted Aztec diamonds. We show that these perfect t-embeddings can be used to prove convergence of gradients of height fluctuations to those of the Gaussian free field.
Tomas Berggren +2 more
semanticscholar +1 more source
Experimental test of the Greenberger–Horne–Zeilinger-type paradoxes in and beyond graph states
npj Quantum Information, 2021 The Greenberger–Horne–Zeilinger (GHZ) paradox is an exquisite no-go theorem that shows the sharp contradiction between classical theory and quantum mechanics by ruling out any local realistic description of quantum theory.
Zheng-Hao Liu +11 more
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The Erdős–Ko–Rado theorem for 2-intersecting families of perfect matchings [PDF]
Algebraic Combinatorics, 2020 A perfect matching in the complete graph on $2k$ vertices is a set of edges such that no two edges have a vertex in common and every vertex is covered exactly once.
Shaun M. Fallat +2 more
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Planar 3-way Edge Perfect Matching Leads to A Holant Dichotomy [PDF]
arXiv.org, 2023 We prove a complexity dichotomy theorem for a class of Holant problems on planar 3-regular bipartite graphs. The complexity dichotomy states that for every weighted constraint function $f$ defining the problem (the weights can even be negative), the ...
Jin-Yi Cai, Austen Z. Fan
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Dirac’s Theorem and Multigraded Syzygies [PDF]
Mediterranean Journal of Mathematics, 2022 Let G be a simple finite graph. A famous theorem of Dirac says that G is chordal if and only if G admits a perfect elimination order. It is known by Fröberg that the edge ideal I ( G ) of G has a linear resolution if and only if the complementary graph $$
A. Ficarra, J. Herzog
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Matchings and Hamilton cycles in hypergraphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 It is well known that every bipartite graph with vertex classes of size $n$ whose minimum degree is at least $n/2$ contains a perfect matching. We prove an analogue of this result for uniform hypergraphs. We also provide an analogue of Dirac's theorem on
Daniela Kühn, Deryk Osthus
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Improved Algorithms for Recognizing Perfect Graphs and Finding Shortest Odd and Even Holes [PDF]
arXiv.org, 2022 An induced subgraph of an n -vertex graph G is a graph that can be obtained by deleting a set of vertices together with its incident edges from G . A hole of G is an induced cycle of G with length at least four. A hole is odd (respectively, even ) if its
Yung-Chung Chiu +2 more
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Limit shape and height fluctuations of random perfect matchings on square-hexagon lattices [PDF]
, 2020 We study asymptotics of perfect matchings on a large class of graphs called the contracting square-hexagon lattice, which is constructed row by row from either a row of a square grid or a row of a hexagonal lattice.
Boutillier, Cédric, Li, Zhongyang
core +3 more sources
On generalisations of the Aharoni–Pouzet base exchange theorem [PDF]
Bulletin of the London Mathematical Society, 2022 The Greene–Magnanti theorem states that if M$ M$ is a finite matroid, B0$ B_0$ and B1$ B_1$ are bases and B0=⋃i=1nXi$ B_0=\bigcup _{i=1}^{n} X_i$ is a partition, then there is a partition B1=⋃i=1nYi$ B_1=\bigcup _{i=1}^{n}Y_i$ such that (B0∖Xi)∪Yi$ (B_0 \
Zsuzsanna Jank'o, Attila Jo'o
semanticscholar +1 more source