The average degree of edge chromatic critical graphs with maximum degree seven
- Resource Type
- Working Paper
- Authors
- Cao, Yan; Luo, Rong; Miao, Zhengke; Zhao, Yue
- Source
- Subject
- Mathematics - Combinatorics
05C15
- Language
In this paper, by developing several new adjacency lemmas about a path on $4$ or $5$ 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 $7$ 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).