On total colorings of 1-planar graphs
Xin Zhang, Jianfeng Hou, Guizhen Liu
TL;DR
This paper proves the total-coloring conjecture for 1-planar graphs with maximum degree at least 13, advancing understanding of coloring properties in nearly planar graphs.
Contribution
It confirms the total-coloring conjecture specifically for 1-planar graphs with high maximum degree, filling a gap in graph coloring theory.
Findings
Confirmed the total-coloring conjecture for 1-planar graphs with maximum degree ≥ 13
Extended total coloring results to a broader class of nearly planar graphs
Provided new techniques for coloring graphs with limited edge crossings
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 with maximum degree at least 13.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Limits and Structures in Graph Theory