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Section A

A generalization of Ramsey theory for linear forests

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Pages 1303-1310 | Received 26 Feb 2011, Accepted 19 Mar 2012, Published online: 11 May 2012
 

Abstract

Chung and Liu defined the d-chromatic Ramsey numbers as a generalization of Ramsey numbers by replacing the usual condition with a slightly weaker condition. Let 1<d<c and let . Assume A 1, A 2, …, A t are all d-subsets of a set containing c distinct colours. Let G 1, G 2, …, G t be graphs. The d-chromatic Ramsey number denoted by is defined as the least number p such that, if the edges of the complete graph K p are coloured in any fashion with c colours, then for some i, the subgraph whose edges are coloured by colours in A i contains a G i . In this paper, we determine for t=3, 4 and for linear forests G i , 1≤it, when G 1 has at most one odd component and G j , 2≤jt−1, either is a path or has no odd component. Consequently, these numbers are determined when G i , 1≤it, is either a path or a stripe.

2010 AMS Subject Classifications :

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