06109953

j

06109953 Wang, Yingqian Xu, Lingji A sufficient condition for a plane graph with maximum degree 6 to be class 1. Discrete Appl. Math. 161, No. 1-2, 307-310 (2013). 2013 Elsevier Science B.V. (North-Holland), Amsterdam EN planar graph conjecture edge coloring maximum degree

doi:10.1016/j.dam.2012.08.011

Summary: A well-known conjecture of Vizing (the planar graph conjecture) states that every plane graph with maximum degree $\Delta \ge 6$ is edge $\Delta $-colorable. Vizing himself showed that every plane graph with maximum degree $\Delta \ge 8$ is edge $\Delta $-colorable. {\it L. Zhang} [Graphs Comb. 16, No. 4, 467--495 (2000; Zbl 0988.05042)] and {\it D. P. Sanders} and {\it Y. Zhao} [J. Comb. Theory, Ser. B 83, No. 2, 201--212 (2001; Zbl 1024.05031)] independently proved that every plane graph with maximum degree 7 is of class 1, i.e., edge 7-colorable. This note shows that every plane graph G with maximum degree 6 is edge 6-colorable if no vertex in $G$ is incident with four faces of size 3.