On total colorings of 1-planar graphs

2013/04/23 by Xin Zhang, Jianfeng Hou, Zhang, Xin +3
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #cs.DM #math.CO

paper · pdf · doi:10.48550/arxiv.1304.6263

arxiv created 2013/04/23 · openalex publication_date 2013/04/23 · arxiv updated 2013/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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