Some multicolor bipartite Ramsey numbers involving cycles and a small number of colors

Johannes H. Hattingh; Ernst J. Joubert

doi:10.1016/j.disc.2018.02.006

Some multicolor bipartite Ramsey numbers involving cycles and a small number of colors

Johannes H. Hattingh, Ernst J. Joubert

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

For bipartite graphs G₁,G₂,…,G_k, the bipartite Ramsey number b(G₁,G₂,…,G_k) is the least positive integer b so that any coloring of the edges of K_b,b with k colors will result in a copy of G_i in the ith color for some i. In this paper, our main focus will be to bound the following numbers: b(C_2t₁,C_2t₂) and b(C_2t₁,C_2t₂,C_2t₃) for all t_i≥3,b(C_2t₁,C_2t₂,C_2t₃,C_2t₄) for 3≤t_i≤9, and b(C_2t₁,C_2t₂,C_2t₃,C_2t₄,C_2t₅) for 3≤t_i≤5. Furthermore, we will also show that these mentioned bounds are generally better than the bounds obtained by using the best known Zarankiewicz-type result.

Original language	English
Pages (from-to)	1325-1330
Number of pages	6
Journal	Discrete Mathematics
Volume	341
Issue number	5
DOIs	https://doi.org/10.1016/j.disc.2018.02.006
Publication status	Published - May 2018

Keywords

Bipartite graph
Cycle
Ramsey

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2018.02.006

Cite this

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title = "Some multicolor bipartite Ramsey numbers involving cycles and a small number of colors",

abstract = "For bipartite graphs G1,G2,…,Gk, the bipartite Ramsey number b(G1,G2,…,Gk) is the least positive integer b so that any coloring of the edges of Kb,b with k colors will result in a copy of Gi in the ith color for some i. In this paper, our main focus will be to bound the following numbers: b(C2t1,C2t2) and b(C2t1,C2t2,C2t3) for all ti≥3,b(C2t1,C2t2,C2t3,C2t4) for 3≤ti≤9, and b(C2t1,C2t2,C2t3,C2t4,C2t5) for 3≤ti≤5. Furthermore, we will also show that these mentioned bounds are generally better than the bounds obtained by using the best known Zarankiewicz-type result.",

keywords = "Bipartite graph, Cycle, Ramsey",

author = "Hattingh, {Johannes H.} and Joubert, {Ernst J.}",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

year = "2018",

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doi = "10.1016/j.disc.2018.02.006",

language = "English",

volume = "341",

pages = "1325--1330",

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T1 - Some multicolor bipartite Ramsey numbers involving cycles and a small number of colors

AU - Hattingh, Johannes H.

AU - Joubert, Ernst J.

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N2 - For bipartite graphs G1,G2,…,Gk, the bipartite Ramsey number b(G1,G2,…,Gk) is the least positive integer b so that any coloring of the edges of Kb,b with k colors will result in a copy of Gi in the ith color for some i. In this paper, our main focus will be to bound the following numbers: b(C2t1,C2t2) and b(C2t1,C2t2,C2t3) for all ti≥3,b(C2t1,C2t2,C2t3,C2t4) for 3≤ti≤9, and b(C2t1,C2t2,C2t3,C2t4,C2t5) for 3≤ti≤5. Furthermore, we will also show that these mentioned bounds are generally better than the bounds obtained by using the best known Zarankiewicz-type result.

AB - For bipartite graphs G1,G2,…,Gk, the bipartite Ramsey number b(G1,G2,…,Gk) is the least positive integer b so that any coloring of the edges of Kb,b with k colors will result in a copy of Gi in the ith color for some i. In this paper, our main focus will be to bound the following numbers: b(C2t1,C2t2) and b(C2t1,C2t2,C2t3) for all ti≥3,b(C2t1,C2t2,C2t3,C2t4) for 3≤ti≤9, and b(C2t1,C2t2,C2t3,C2t4,C2t5) for 3≤ti≤5. Furthermore, we will also show that these mentioned bounds are generally better than the bounds obtained by using the best known Zarankiewicz-type result.

KW - Bipartite graph

KW - Cycle

KW - Ramsey

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JO - Discrete Mathematics

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ER -

Some multicolor bipartite Ramsey numbers involving cycles and a small number of colors

Abstract

Keywords

ASJC Scopus subject areas

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