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On ramsey numbers for large disjoint unions of graphs

Authors
Journal
Discrete Mathematics
0012-365X
Publisher
Elsevier
Publication Date
Volume
70
Issue
3
Identifiers
DOI: 10.1016/0012-365x(88)90004-0

Abstract

Abstract Let G be a fixed finite set of connected graphs. Results are given which, in principle, permit the Ramsey number r( G, H) to be evaluated exactly when G and H are sufficiently large disjoint unions of graphs taken from G . Such evaluations are often possible in practice, as shown by several examples. For instance, when m and n are large, and m⩽ n, r(mK k, nK l)=(k − 1)m+ln+r(K k−1, K l−1)−2.

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