A generalization of Ramsey theory for stars and one matching

2012/03/11 by Khamseh, Amir, Omidi, Gholamreza · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1203.2339

Abstract

A recent question in generalized Ramsey theory is that for fixed positive integers s≤ t, at least how many vertices can be covered by the vertices of no more than s monochromatic members of the family \cal F in every edge coloring of K_n with t colors. This is related to d-chromatic Ramsey numbers introduced by Chung and Liu. In this paper, we first compute these numbers for stars generalizing the well-known result of Burr and Roberts. Then we extend a result of Cockayne and Lorimer to compute d-chromatic Ramsey numbers for stars and one matching.

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• The d-chromatic Ramsey number for stars

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