数学物理学报(英文版) ›› 1996, Vol. 16 ›› Issue (2): 162-169.
许宝刚
Xu Baogang
摘要: The total chromatic number XT(G) of graph G is the least number of colors assigned to VE(G) such that no adjacent or incident elements receive the same color.Given graphs G1,G2, the join of G1 and G2, denoted by G1∨G2, is a graph G, V(G)=V(G1)∪V(G2) and E(G)=E(G1)∪E(G2) ∪{uv|u∈V(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(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.