[r,s,t]-Coloring of the Bipatite graph
Xinjun Zhang · Journal of Chongqing University. English Edition · 2007
A.Kemnitz and M.Marangio first give us the concept of [r,s,t]-colorings,it is a generalization of the classical graph colorings,such as proper vertex coloring,edge coloring and total coloring.In this paper,we obtain the bounds of the [r,s,t]-chromatic number of the bigraph and the conditions of the lower bound achieved,talking about the [r,s,t]-chromatic number of the star,we get the main results as follows:1)If G is bipartite graph,v1,v2∈VΔ,v1v2E(G),for all u∈VΔ,there exists u1∈NG(u) makes dG(u1)=1 and s≥2t,r≤t,then χr,s,t(G)=(Δ-1)s+1.2) If G is bipartite graph and r≥(Δ-1)s+2t,then χr,s,t(G)=r+1.3) If G is bipartite graph and(Δ-1)s+tr≤(Δ-1)s+2t,then χr,s,t(G)≤(Δ-1)s+2t+1.4) If G is bipartite graph,then rΔ+1≤χr,r,r(G)≤r(Δ+1)+1.