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|Abstract:||We prove that for all integers K, s >= 0 there exists c with the following property. Let G be a graph with clique number at most K and chromatic number more than c. Then for every vertex-colouring (not necessarily optimal) of G, some induced subgraph of G is an s-vertex path, and all its vertices have different colours. This extends a recent result of Gyarfas and Sarkozy (2016), who proved the same for graphs G with K = 2 and girth at least five.|
|Electronic Publication Date:||30-Jun-2017|
|Citation:||Scott, Alex, Seymour, Paul. (2017). Induced subgraphs of graphs with large chromatic number IX: Rainbow paths. ELECTRONIC JOURNAL OF COMBINATORICS, 24|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||ELECTRONIC JOURNAL OF COMBINATORICS|
|Version:||Final published version. This is an open access article.|
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