Acyclic coloring of IC-planar graphs

Acyclic coloring of IC-planar graphs

A graph G is called an IC-planar graph if it can be embedded in the plane so that every edge is crossed by at most one other edge and every vertex is incident to at most one crossing edge. In this paper, we prove that every IC-planar graph is acyclically 10-colorable. Moreover, an IC-planar graph of...

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Veröffentlicht in:Discrete mathematics 2019-12, Vol.342 (12), p.111623, Article 111623
Hauptverfasser: Yang, Wanshun, Wang, Weifan, Wang, Yiqiao
Format: Artikel
Sprache:eng
Schlagworte:
1-planar graph
Acyclic chromatic number
Acyclic coloring
IC-planar graph
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Zusammenfassung:A graph G is called an IC-planar graph if it can be embedded in the plane so that every edge is crossed by at most one other edge and every vertex is incident to at most one crossing edge. In this paper, we prove that every IC-planar graph is acyclically 10-colorable. Moreover, an IC-planar graph of the acyclic chromatic number 6 is constructed.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2019.111623