The average degree of edge chromatic critical graphs with maximum degree seven
Combinatorics
2023-01-06 v1
Abstract
In this paper, by developing several new adjacency lemmas about a path on or vertices, we show that the average degree of 7-critical graphs is at least 6. It implies Vizing's planar graph conjecture for planar graphs with maximum degree and its extension to graphs embeddable in a surface with nonnegative Euler characteristic due to Sanders and Zhao (J. Combin. Theory Ser. B 83 (2001) 201-212 and J. Combin. Theory Ser. B 87 (2003) 254-263) and Zhang (Graphs and Combinatorics 16 (2000) 467-495).
Keywords
Cite
@article{arxiv.2301.02140,
title = {The average degree of edge chromatic critical graphs with maximum degree seven},
author = {Yan Cao and Rong Luo and Zhengke Miao and Yue Zhao},
journal= {arXiv preprint arXiv:2301.02140},
year = {2023}
}