On multicolour noncomplete Ramsey graphs of star graphs

Given graphs G, G(1),...,G(k), where k >= 2, the notation G --> (G(1), G(2),...,G(k)) denotes that every factorization F-1 circle plus F-2 circle plus ... circle plus F-k of G implies G(i) subset of F-i for at least one i, 1 <= i <= k. We characterize G for which G --> (K (1, n(1)), K(1, n(2)),...,K(1, n(k))) and derive some consequences from this. In particular, this gives the value of the graph Ramsey number R(K(1, n(1)), K(1, n(2)),..., K (1, n(k))). (C) 2007 Elsevier B.V. All rights reserved.