Publication details

Edge colorings avoiding patterns

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DEBSKI Michal Karol

Year of publication 2019
Type Article in Periodical
Magazine / Source Acta Mathematica Universitatis Comenianae
MU Faculty or unit

Faculty of Informatics

Keywords edge coloring; entropy compression
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Description We say that a pattern is a graph together with an edge coloring, and a pattern P = (H, c) occurs in some edge coloring c' of G if c', restricted to some subgraph of G isomorphic to H, is equal to c up to renaming the colors. Inspired by Matousek's visibility blocking problem, we study edge colorings of cliques that avoid certain patterns. We show that for every pattern P, such that the number of edges in P is at least the number of vertices in P plus the number of colors minus 2, there is an edge coloring of K-n that avoids P and uses linear number of colors; the same also holds for finite sets of such patterns.
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