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- W1768608265 abstract "Given an edge coloring of a graph with a set of m colors, we say that the graph is exactly m-colored if each of the colors is used. In 1999, Stacey and Weidl, partially resolving a conjecture of Erickson from 1994, showed that for a fixed natural number and for all sufficiently large k, there is a k-coloring of the complete graph on such that no complete infinite subgraph is exactly m-colored. In the light of this result, we consider the question of how close we can come to finding an exactly m-colored complete infinite subgraph. We show that for a natural number m and any finite coloring of the edges of the complete graph on with m or more colors, there is an exactly -colored complete infinite subgraph for some satisfying ; this is best possible up to the additive constant. We also obtain analogous results for this problem in the setting of r-uniform hypergraphs. Along the way, we also prove a recent conjecture of the second author and investigate generalizations of this conjecture to r-uniform hypergraphs." @default.
- W1768608265 created "2016-06-24" @default.
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- W1768608265 date "2015-01-14" @default.
- W1768608265 modified "2023-09-23" @default.
- W1768608265 title "Approximations tom-Colored Complete Infinite Hypergraphs" @default.
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- W1768608265 doi "https://doi.org/10.1002/jgt.21853" @default.
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