A relaxation of the Bordeaux Conjecture

Abstract

A $(c_1,c_2,...,c_k)$-coloring of $G$ is a mapping $\phi :V(G)\mapsto \{1,2,...,k\}$ such that for every $i,1\le i\le k$, $G[V_i]$ 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.

The paper is accepted by European Journal of Combinatorics for publication

References in corpus (1)

• Planar graphs without 5-cycles and intersecting triangles are $(1,1,0)$-colorable

Cited by in corpus (1)

• Planar graphs without 5-cycles and intersecting triangles are $(1,1,0)$-colorable