ON THE TOTAL COLORING OF GRAPH G ∨H

作     者：许宝刚 

作者机构：Math. of Dept. Shandong University Jinan 250100 China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：1996年第16卷第2期

页      面：162-169页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：graph join of graphs total chromatic number. 

摘      要：The total chromatic number XT(G) of graph G is the least number of colorsassigned to VE(G) such that no adjacent or incident elements receive the same *** graphs G1,G2, the join of G1 and G2, denoted by G1∨G2, is a graph G, V(G) =V(GI)∪V(G2) and E(G) = E(G1)∪E(G2) ∪{uv | u∈(G1), v ∈ V(G2)}. In this paper, it s proved that if v(G) = v(H), both Gc and Hc contain perfect matching and one of the followings holds: (i)Δ(G) =Δ(H) and there exist edge e∈ E(G), e E E(H)such that both G-e and H-e are of Class l; (ii)Δ(G)Δ(H) and there exixst an edge e ∈E(H) such that H-e is of Class 1, then, the total coloring conjecture is true for graph G ∨H.