Planar Graphs of Maximum Degree Seven are Class I

In 1965, Vizing proved that planar graphs of maximum degree at least eight have the edge chromatic number equal to their maximum degree. He conjectured the same if the maximum degree is either six or seven. This article proves the maximum degree seven case.

[1]  Yue Zhao,et al.  On total 9-coloring planar graphs of maximum degree seven , 1999, J. Graph Theory.

[2]  Tommy R. Jensen,et al.  Graph Coloring Problems , 1994 .

[3]  Robin Thomas,et al.  The Four-Colour Theorem , 1997, J. Comb. Theory, Ser. B.

[4]  Yue Zhao,et al.  On Improving the Edge-Face Coloring Theorem , 2001, Graphs Comb..