Results 51 to 60 of about 4,692 (164)
Multicolor bipartite Ramsey number of double stars
, 2023 For positive integers $n, m$, the double star $S(n,m)$ is the graph consisting of the disjoint union of two stars $K_{1,n}$ and $K_{1,m}$ together with an edge joining their centers. Finding monochromatic copies of double stars in edge-colored complete bipartite graphs has attracted much attention.
DeCamillis, Gregory, Song, Zi-Xia
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The m-bipartite Ramsey number of the K2,2 versus K6,6 [PDF]
Contributions to Mathematics, 2022 Yaser Rowshan
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Weighted Turán Theorems With Applications to Ramsey‐Turán Type of Problems
Journal of Graph Theory, Volume 110, Issue 1, Page 59-71, September 2025.ABSTRACT We study extensions of Turán Theorem in edge‐weighted settings. A particular case of interest is when constraints on the weight of an edge come from the order of the largest clique containing it. These problems are motivated by Ramsey‐Turán type problems.
József Balogh +2 more
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Bipartite Ramsey Numbers for Graphs of Small Bandwidth
The Electronic Journal of Combinatorics, 2018 A graph $H=(W,E_H)$ is said to have bandwidth at most $b$ if there exists a labeling of $W$ as $w_1,w_2,\dots,w_n$ such that $|i-j|\leq b$ for every edge $w_iw_j\in E_H$, and a bipartite balanced $(\beta,\Delta)$-graph $H$ is a bipartite graph with bandwidth at most $\beta |W|$ and maximum degree at most $\Delta$, and furthermore it has a proper 2 ...
Shen, Lili, Lin, Qizhong, Liu, Qinghai
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Combinatorial theorems relative to a random set [PDF]
, 2014 We describe recent advances in the study of random analogues of combinatorial theorems.Comment: 26 pages.
Conlon, David
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Journal of Graph Theory, Volume 110, Issue 1, Page 82-91, September 2025.ABSTRACT An inversion of a tournament T is obtained by reversing the direction of all edges with both endpoints in some set of vertices. Let inv k ( T ) be the minimum length of a sequence of inversions using sets of size at most k that result in the transitive tournament.
Raphael Yuster
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On the Geometric Ramsey Number of Outerplanar Graphs
, 2013 We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2 outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey numbers of the ladder graph on $2n$ vertices are bounded by $O(n^{3})$ and $O(
Cibulka, Josef +4 more
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A Sharper Ramsey Theorem for Constrained Drawings
Journal of Graph Theory, Volume 109, Issue 4, Page 401-411, August 2025.ABSTRACT Given a graph G and a collection C of subsets of R d indexed by the subsets of vertices of G, a constrained drawing of G is a drawing where each edge is drawn inside some set from C, in such a way that nonadjacent edges are drawn in sets with disjoint indices. In this paper we prove a Ramsey‐type result for such drawings.
Pavel Paták
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Canonical colourings in random graphs
Journal of the London Mathematical Society, Volume 112, Issue 2, August 2025.Abstract Rödl and Ruciński (J. Amer. Math. Soc. 8 (1995), 917–942) established Ramsey's theorem for random graphs. In particular, for fixed integers r$r$, ℓ⩾2$\ell \geqslant 2$ they proved that p̂Kℓ,r(n)=n−2ℓ+1$\hat{p}_{K_\ell,r}(n)=n^{-\frac{2}{\ell +1}}$ is a threshold for the Ramsey property that every r$r$‐colouring of the edges of the binomial ...
Nina Kamčev, Mathias Schacht
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On the path-complete bipartite Ramsey number
Discrete Mathematics, 1989 Publisher Summary Let r(P k , K n,m ) denote the (mixed) Ramsey number between a path Pk on k vertices and a K n,m . Thus r(P k , K n,m ) is the minimal number such that every graph G on r(P k , K n,m ) vertices either contains a Pk, or else contains a K n,m in the complement G. The chapter proves the theorem r(P k , K n ,m ) ≤ n
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