On the cycle-path bipartite Ramsey number

Ernst J. Joubert; Michael A. Henning

doi:10.1016/j.disc.2023.113759

On the cycle-path bipartite Ramsey number

Ernst J. Joubert, Michael A. Henning

Mathematics and Applied Mathematics

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

1 Citation (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 we will show that if s is an integer such that s≥max⁡{18,(b(C₃₄,C₃₄)+1)/2}, then b(C_2s,P_2s)=2s−1.

Original language	English
Article number	113759
Journal	Discrete Mathematics
Volume	347
Issue number	2
DOIs	https://doi.org/10.1016/j.disc.2023.113759
Publication status	Published - Feb 2024

Keywords

Bipartite graph
Cycle
Path
Ramsey

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2023.113759

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title = "On the cycle-path bipartite Ramsey number",

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 we will show that if s is an integer such that s≥max⁡{18,(b(C34,C34)+1)/2}, then b(C2s,P2s)=2s−1.",

keywords = "Bipartite graph, Cycle, Path, Ramsey",

author = "Joubert, {Ernst J.} and Henning, {Michael A.}",

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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 we will show that if s is an integer such that s≥max⁡{18,(b(C34,C34)+1)/2}, then b(C2s,P2s)=2s−1.

KW - Bipartite graph

KW - Cycle

KW - Path

KW - Ramsey

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On the cycle-path bipartite Ramsey number

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Keywords

ASJC Scopus subject areas

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