Year: 2025
Type: article
Abstract: ABSTRACT We prove that for any graph , the total chromatic number of is at most . This saves one color in comparison with the result of Hind from 1992. In particular, our result says that if , then has a total coloring using at most colors. When is regular and has a sufficient number of vertices, we can actually save an additional two colors. Specifically, we prove that for any , there exists such that: if is an ‐regular graph on vertices with , then . This confirms the Total Coloring Conjecture for such graphs .
Source: Journal of Graph Theory
DOI: 10.1002/jgt.23268
Authors: Aseem Dalal, Jessica McDonald, Songling Shan
Institutions: Indian Institute of Technology Delhi, Auburn University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4411217974