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arXiv · 1407.5138

A relaxation of the Bordeaux Conjecture

Runrun Liu·Xiangwen Li·Gexin Yu
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Abstract

A $(c_1,c_2,...,c_k)$-coloring of $G$ is a mapping $φ:V(G)\mapsto\{1,2,...,k\}$ such that for every $i,1 \leq i \leq k$, $G[V_i]$ has maximum degree at most $c_i$, where $G[V_i]$ denotes the subgraph induced by the vertices colored $i$. Borodin and Raspaud conjecture that every planar graph without intersecting triangles and $5$-cycles is $3$-colorable. We prove in this paper that every planar graph without intersecting triangles and $5$-cycles is (2,0,0)-colorable.

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Runrun Liu, Xiangwen Li, Gexin Yu. 2015-04-06. A relaxation of the Bordeaux Conjecture. https://arxiv.org/abs/1407.5138

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