图的某些[r,s,t]-染色的色数

Some -chromatic number of graphs

证明了(1)若图G是二部图,则当r≥s(χ'(G)-1)+2时,χr,s,1(G)=χr,0,0(G);(2)若图G是非二部图,则当r≥sχ'(G)/χ(G)-s+1且r不是s的倍数时,χr,s,1(G)=χr,0,0(G);(3)当Δ(G)≥2,χ'(G)=Δ(G),且s≥2r,r≥2t时,χr,s,t(G)=χ0,s,0(G);(4)当χ'(G)=Δ(G)+1且s-t≥r≥t时,χr,s,t(G)=χ0,s,0(G)。

It is proved that（1） if G is a bipartite graph and r≥s（χ′（G）-1）＋2,then χr,s,1（G）=χr,0,0（G）;（2） if G is a non-bipartite graph and r≥s χ′（G）/ χ（G）-s＋1 and r is not a multiple of s,then χr,s,1（G）=χr,0,0（G）;（3） when Δ（G）≥2,χ′（G）=Δ（G） and s≥2r,r≥2t,then χr,s,t（G）=χ0,s,0（G）;（4） when χ′（G）=Δ（G）＋1 and s-t≥r≥t then χr,s,t（G）=χ0,s,0（G）.