Planar Graphs of Maximum Degree 6 and without Adjacent 8-Cycles Are 6-Edge-Colorable

Table 1

Symbols of graphs.

	The set of all edges incident with
	Cardinality of
	Neighbor set of
-, -, -vertex	Vertex with , , or
-, -neighbor of a vertex	- or -vertex adjacent to
-cycle	Cycle of length
	The set of all faces of a planar graph
	Number of edges on with each cut edge calculated twice
-, -face	Face with ,
	Number of -faces incident with
	Number of -neighbors of
	i-th smallest degree of a neighbor of
	Length of the shortest cycle of a graph