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arXiv · 2205.11125

Majority Edge-Colorings of Graphs

Felix Bock·Rafał Kalinowski·Johannes Pardey·Monika Pilśniak·Dieter Rautenbach·Mariusz Woźniak
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Abstract

We propose the notion of a majority $k$-edge-coloring of a graph $G$, which is an edge-coloring of $G$ with $k$ colors such that, for every vertex $u$ of $G$, at most half the edges of $G$ incident with $u$ have the same color. We show the best possible results that every graph of minimum degree at least $2$ has a majority $4$-edge-coloring, and that every graph of minimum degree at least $4$ has a majority $3$-edge-coloring. Furthermore, we discuss a natural variation of majority edge-colorings and some related open problems.

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Felix Bock, Rafał Kalinowski, Johannes Pardey, Monika Pilśniak, Dieter Rautenbach, Mariusz Woźniak. 2022-05-23. Majority Edge-Colorings of Graphs. https://arxiv.org/abs/2205.11125

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