Some Generalized Bipartite Ramsey Numbers Involving Short Cycles

Ernst J. Joubert

doi:10.1007/s00373-017-1761-z

Some Generalized Bipartite Ramsey Numbers Involving Short Cycles

Ernst J. Joubert

Mathematics and Applied Mathematics

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

7 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 colouring of the edges of K_b _, _b with k colours will result in a copy of G_i in the ith colour for some i. In this paper, we will consider the bipartite Ramsey number b(C2t1,C2t2,…,C2tk), where t_i is an integer and 2 ≤ t_i≤ 4 , for all 1 ≤ i≤ k. In particular, we will show that b(C2t1,C2t2,…,C2tk)≤ k(t₁+ t₂+ ⋯ + t_k- k+ 1).

Original language	English
Pages (from-to)	433-448
Number of pages	16
Journal	Graphs and Combinatorics
Volume	33
Issue number	2
DOIs	https://doi.org/10.1007/s00373-017-1761-z
Publication status	Published - 1 Mar 2017

Keywords

Bipartite graph
Cycle
Ramsey

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1007/s00373-017-1761-z

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title = "Some Generalized Bipartite Ramsey Numbers Involving Short Cycles",

abstract = "For bipartite graphs G1, G2, … , Gk, the bipartite Ramsey number b(G1, G2, … , Gk) is the least positive integer b so that any colouring of the edges of Kb , b with k colours will result in a copy of Gi in the ith colour for some i. In this paper, we will consider the bipartite Ramsey number b(C2t1,C2t2,…,C2tk), where ti is an integer and 2 ≤ ti≤ 4 , for all 1 ≤ i≤ k. In particular, we will show that b(C2t1,C2t2,…,C2tk)≤ k(t1+ t2+ ⋯ + tk- k+ 1).",

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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 colouring of the edges of Kb , b with k colours will result in a copy of Gi in the ith colour for some i. In this paper, we will consider the bipartite Ramsey number b(C2t1,C2t2,…,C2tk), where ti is an integer and 2 ≤ ti≤ 4 , for all 1 ≤ i≤ k. In particular, we will show that b(C2t1,C2t2,…,C2tk)≤ k(t1+ t2+ ⋯ + tk- k+ 1).

KW - Bipartite graph

KW - Cycle

KW - Ramsey

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JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

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ER -

Some Generalized Bipartite Ramsey Numbers Involving Short Cycles

Abstract

Keywords

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