The upper domination Ramsey number u(3,3,3)

Michael A. Henning; Ortrud R. Oellermann

doi:10.1016/S0012-365X(00)00369-1

The upper domination Ramsey number u(3,3,3)

Michael A. Henning, Ortrud R. Oellermann

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

6 Citations (Scopus)

Abstract

Let G1, G2,...,G_t be an arbitrary t-edge colouring of K_n, where for each i ∈{1,2,...,t}, G_i is the spanning subgraph of K_n consisting of all edges coloured with colour i. The upper domination Ramsey number u(n₁,n₂,...,n_t) is defined as the smallest n such that for every t-edge colouring G₁,G₂,...,G₁ of K_n, there is at least one i ∈ {1,2,...,t} for which G_i, has upper domination number at least n_i. We show that 13≤u(3,3,3)≤14.

Original language	English
Pages (from-to)	103-113
Number of pages	11
Journal	Discrete Mathematics
Volume	242
Issue number	1-3
DOIs	https://doi.org/10.1016/S0012-365X(00)00369-1
Publication status	Published - 1 Jun 2002
Externally published	Yes

Keywords

Upper domination ramsey numbers

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/S0012-365X(00)00369-1

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N2 - Let G1, G2,...,Gt be an arbitrary t-edge colouring of Kn, where for each i ∈{1,2,...,t}, Gi is the spanning subgraph of Kn consisting of all edges coloured with colour i. The upper domination Ramsey number u(n1,n2,...,nt) is defined as the smallest n such that for every t-edge colouring G1,G2,...,G1 of Kn, there is at least one i ∈ {1,2,...,t} for which Gi, has upper domination number at least ni. We show that 13≤u(3,3,3)≤14.

AB - Let G1, G2,...,Gt be an arbitrary t-edge colouring of Kn, where for each i ∈{1,2,...,t}, Gi is the spanning subgraph of Kn consisting of all edges coloured with colour i. The upper domination Ramsey number u(n1,n2,...,nt) is defined as the smallest n such that for every t-edge colouring G1,G2,...,G1 of Kn, there is at least one i ∈ {1,2,...,t} for which Gi, has upper domination number at least ni. We show that 13≤u(3,3,3)≤14.

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The upper domination Ramsey number u(3,3,3)

Abstract

Keywords

ASJC Scopus subject areas

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