Single-conflict colorings of degenerate graphs

12/12/2021

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by   Peter Bradshaw, et al.

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We consider single-conflict colorings, a variant of graph colorings in which each edge of a graph has a single forbidden color pair. We show that for any assignment of forbidden color pairs to the edges of a d-degenerate graph G on n vertices of edge-multiplicity at most loglog n, O(√( d )log n) colors are always enough to color the vertices of G in a way that avoids every forbidden color pair. This answers a question of Dvořák, Esperet, Kang, and Ozeki for simple graphs (Journal of Graph Theory 2021).