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arXiv · 1701.03007

Decomposing edge-colored graphs under color degree constraints

Ruonan Li·Shinya Fujita·Guanghui Wang
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Abstract

For an edge-colored graph $G$, the minimum color degree of $G$ means the minimum number of colors on edges which are adjacent to each vertex of $G$. We prove that if $G$ is an edge-colored graph with minimum color degree at least $5$ then $V(G)$ can be partitioned into two parts such that each part induces a subgraph with minimum color degree at least $2$. We show this theorem by proving a much stronger form. Moreover, we point out an important relationship between our theorem and Bermond-Thomassen's conjecture in digraphs.

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Ruonan Li, Shinya Fujita, Guanghui Wang. 2017-01-11. Decomposing edge-colored graphs under color degree constraints. https://arxiv.org/abs/1701.03007

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