Rainbow Subgraphs in Edge-Colorings of Complete Graphs

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Abstract

We raise the following problem. Let F be a given graph with e edges. Consider the edge colorings of Kn(n large) with e colors, such that every vertex has degree at least d in each color (d<n/e). For which values of d does every such edge coloring contain a subgraph isomorphic to F, all of whose edges have distinct colors? The case when F is the triangle K3is well-understood, but for other graphs F many interesting questions remain open, even for d-regular colorings when n = de + 1. © 1993, Elsevier Science & Technology.

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Erdős, P., & Tuza, Z. (1993). Rainbow Subgraphs in Edge-Colorings of Complete Graphs. Annals of Discrete Mathematics, 55(C), 81–88. https://doi.org/10.1016/S0167-5060(08)70377-7

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