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 K3 is well-understood, but for other graphs F many interesting questions remain open, even for d-regular colorings when n = de + 1.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics