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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 791.05037

**Autor: ** Erdös, Paul; Tuza, Zsolt

**Title: ** Rainbow subgraphs in edge-colorings of complete graphs. (In English)

**Source: ** Gimbel, John (ed.) et al., Quo vadis, graph theory? A source book for challenges and directions. Amsterdam: North-Holland, Ann. Discrete Math. 55, 81-88 (1993).

**Review: ** We raise the following problem. Let F be a given graph with e edges. Consider the edge colorings of K_{n} (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 K_{3} is well-understood, but for other graphs F many interesting questions remain open, even for d-regular colorings when n = de+1.

**Classif.: ** * 05C15 Chromatic theory of graphs and maps

**Keywords: ** rainbow subgraphs; complete graphs; edge colorings

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