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Ramsey numbers and bipartite Ramsey numbers via quasi-random graphs

Discrete Mathematics, 2021
In this paper we show that r ( C 4 , K t , t ) ≥ Ω ( t 3 ∕ 2 log t ) via quasi-random graphs giving a polylogarithmic improvement over the currently best lower bound, which implies r ( C 4 , K t ) ≥ Ω ( t 3 ∕ 2 log t ) and b r ( C 4 , K t , t ) ≥ Ω ( t 3
Meng Liu, Yusheng Li
semanticscholar   +2 more sources

On the cycle-path bipartite Ramsey number

Discrete Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ernst J. Joubert, Michael A. Henning
semanticscholar   +2 more sources

Some Generalized Bipartite Ramsey Numbers Involving Short Cycles

Graphs and Combinatorics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
E. J. Joubert
semanticscholar   +3 more sources

A Note on the Multi-Colored Bipartite Ramsey Number for Paths

J. Interconnect. Networks, 2021
For bipartite graphs [Formula: see text], the bipartite Ramsey number [Formula: see text] is the least positive integer [Formula: see text] so that any coloring of the edges of [Formula: see text] with [Formula: see text] colors will result in a copy of [
Hanxiao Qiao   +3 more
semanticscholar   +1 more source

Three‐colored asymmetric bipartite Ramsey number of connected matchings and cycles

Journal of Graph Theory, 2020
Guaranteed by Szemerédi's Regularity Lemma, a technique originated by Łuczak is to reduce the problem of showing the existence of a monochromatic cycle to show the existence of a monochromatic matching in a component.
Zhidan Luo, Yuejian Peng
semanticscholar   +1 more source

Some Bistar Bipartite Ramsey Numbers

Graphs and Combinatorics, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hattingh, Johannes H., Joubert, Ernst J.
openaire   +1 more source

Note on the three-coloured bipartite Ramsey numbers for paths

International Journal of Computer Mathematics Computer Systems Theory, 2021
For bipartite graphs , the bipartite Ramsey number is the least positive integer p so that any coloring of the edges of with k colors will result in a copy of in the ith color for some i.
Ke Wang, Jiannan Zhou, Dong He, Qin Tong
semanticscholar   +1 more source

Bipartite anti‐Ramsey numbers of cycles

Journal of Graph Theory, 2004
AbstractWe determine the maximum number of colors in a coloring of the edges of Km,n such that every cycle of length 2k contains at least two edges of the same color. One of our main tools is a result on generalized path covers in balanced bipartite graphs.
Axenovich, Maria   +2 more
openaire   +2 more sources

Three-Color Ramsey Number of an Odd Cycle Versus Bipartite Graphs with Small Bandwidth

Graphs and Combinatorics, 2022
A graph $$\mathcal {H}=(W,E_\mathcal {H})$$ H = ( W , E H ) is said to have bandwidth at most b if there exists a labeling of W as $$w_1,w_2,\dots ,w_n$$ w 1 , w 2 , ⋯ , w n such that $$|i-j|\le b$$ | i - j | ≤ b for every edge $$w_iw_j\in E_\mathcal {H}$
Chunlin You, Qizhong Lin
semanticscholar   +1 more source

Bipartite Ramsey Numbers of Cycles for Random Graphs

Graphs and Combinatorics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Meng, Li, Yusheng
openaire   +1 more source

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