Combinatorics, Probability and Computing
Extensions of Gallai–Ramsey results
Journal of Graph Theory
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Motivated by questions in Ramsey theory, we consider colorings of the edges of the complete graph Kn that contain no rainbow path Pt+1 of length t. If fewer than t colors are used then certainly there is no rainbow Pt+1. We show that, if at least t colors are used, then very few colorings are possible if t ≤ 5 and these can be described precisely, whereas the situation for t ≥ 6 is qualitatively different. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 261–266, 2007