The average degree of edge chromatic critical graphs with maximum degree seven.

In this paper, by developing several new adjacency lemmas about a path on four or five 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, and Zhang. [ABSTRACT FROM AUTHOR]