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Published in:
13-03-2020
Plane graphs with \(\Delta =7\) are entirely 10-colorable
Published in: Journal of Combinatorial Optimization | Issue 1/2020
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Abstract
A plane graph G is entirely k-colorable if \(V(G)\cup E(G) \cup F(G)\) can be colored with k colors such that any two adjacent or incident elements receive different colors. In 2011, Wang and Zhu conjectured that every plane graph G with maximum degree \(\Delta \ge 3\) and \(G\ne K_4\) is entirely \((\Delta +3)\)-colorable. It is known that the conjecture holds for the case \(\Delta \ge 8\). The condition \(\Delta \ge 8\) is improved to \(\Delta \ge 7\) in this paper.