Results 1 to 10 of about 414,884 (100)
Lobsters with an almost perfect matching are graceful [PDF]
, 2014 Let $T$ be a lobster with a matching that covers all but one vertex.
Krop, Elliot
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Almost color-balanced perfect matchings in color-balanced complete graphs [PDF]
Discrete Mathematics, 2022 For a graph $G$ and a not necessarily proper $k$-edge coloring $c:E(G)\to \{ 1,\ldots,k\}$, let $m_i(G)$ be the number of edges of $G$ of color $i$, and call $G$ {\it color-balanced} if $m_i(G)=m_j(G)$ for every two colors $i$ and $j$. Several famous open problems relate to this notion; Ryser's conjecture on transversals in latin squares, for instance,
Pardey, Johannes, Rautenbach, Dieter
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Almost Perfect Matchings in $k$-Partite $k$-Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2018 The minimum co-degree threshold for a perfect matching in a $k$-graph with $n$ vertices was determined by R dl, Ruci ski and Szemer di for the case when $n\equiv 0\pmod k$. Recently, Han resolved the remaining cases when $n \not\equiv 0\pmod k$, establishing a conjecture of R dl, Ruci ski and Szemer di.
Lu, Hongliang, Wang, Yan, Yu, Xingxing
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Matching Is as Easy as the Decision Problem, in the NC Model [PDF]
, 2020 Is matching in NC, i.e., is there a deterministic fast parallel algorithm for it? This has been an outstanding open question in TCS for over three decades, ever since the discovery of randomized NC matching algorithms [KUW85, MVV87].
Anari, Nima, Vazirani, Vijay V.
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New bounds on the size of nearly perfect matchings in almost regular hypergraphs
Journal of the London Mathematical Society, 2023 AbstractLet be a ‐uniform ‐regular simple hypergraph on vertices. Based on an analysis of the Rödl nibble, in 1997, Alon, Kim and Spencer proved that if , then contains a matching covering all but at most vertices, and asked whether this bound is tight. In this paper we improve their bound by showing that for all , contains a matching covering all
Kang, Dong Yeap +3 more
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Almost all Steiner triple systems have perfect matchings [PDF]
Proceedings of the London Mathematical Society, 2020 We show that for any n divisible by 3, almost all order-n Steiner triple systems have a perfect matching (also known as a parallel class or resolution class). In fact, we prove a general upper bound on the number of perfect matchings in a Steiner triple system and show that almost all Steiner triple systems essentially attain this maximum.
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Finding an almost perfect matching in a hypergraph avoiding forbidden submatchings
, 2022 In 1973, Erdős conjectured the existence of high girth $(n,3,2)$-Steiner systems. Recently, Glock, Kühn, Lo, and Osthus and independently Bohman and Warnke proved the approximate version of Erdős' conjecture. Just this year, Kwan, Sah, Sawhney, and Simkin proved Erdős' conjecture.
Delcourt, Michelle, Postle, Luke
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The typical structure of maximal triangle-free graphs [PDF]
, 2015 Recently, settling a question of Erd\H{o}s, Balogh and Pet\v{r}\'{i}\v{c}kov\'{a} showed that there are at most $2^{n^2/8+o(n^2)}$ $n$-vertex maximal triangle-free graphs, matching the previously known lower bound.
Balogh, József +3 more
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On the Key-Uncertainty of Quantum Ciphers and the Computational Security of One-way Quantum Transmission [PDF]
, 2004 We consider the scenario where Alice wants to send a secret (classical) $n$-bit message to Bob using a classical key, and where only one-way transmission from Alice to Bob is possible.
D. DiVincenzo +5 more
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Bipartite Perfect Matching in Pseudo-Deterministic NC [PDF]
, 2017 We present a pseudo-deterministic NC algorithm for finding perfect matchings in bipartite graphs. Specifically, our algorithm is a randomized parallel algorithm which uses poly(n) processors, poly(log n) depth, poly(log n) random bits, and outputs for ...
Goldwasser, Shafi, Grossman, Ofer
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