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arXiv · 2312.05564

Majority distinguishing edge coloring

Aleksandra Gorzkowska·Magdalena Prorok
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Abstract

We consider edge colorings of graphs. An edge coloring is a majority coloring if for every vertex at most half of the edges incident with it are in one color. And edge coloring is a distinguishing coloring if for every non-trivial automorphism at least one edge changes its color. We consider these two notions together. We show that every graph without pendant edges has a majority distinguishing edge coloring with at most $\lceil\sqrtΔ\rceil+5$ colors. Moreover, we show results for some classes of graphs and a~general result for symmetric digraphs.

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Aleksandra Gorzkowska, Magdalena Prorok. 2023-12-09. Majority distinguishing edge coloring. https://arxiv.org/abs/2312.05564

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