Contents

Ars Combinatoria

  • Research article

On total coloring of 1-planar graphs without 4-cycles

Wei-Ping Ni1, Wen-yao Song1
1School of Mathematics and Statistics, Zaozhuang University, Shandong, 277160, China
  • Accepted: 10/06/2020
  • Published Online: 22/03/2025

Abstract

A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we confirm the total-coloring conjecture for 1-planar graphs without 4-cycles with maximum degree \(\Delta\geq10\).

Keywords: planar graphs, graph coloring, planar graph theory, edge crossings
Information
Guidelines
CP Initiatives
Follow CP
Facebook X-twitter Linkedin

1970-2025 CP (Manitoba, Canada) unless otherwise stated.

Citation
Wei-Ping Ni, Wen-yao Song. On total coloring of 1-planar graphs without 4-cycles[J], Ars Combinatoria, Volume 162. 83-91. https://doi.org/10.61091/ars162-07.