Let G be a graph.We useχ(G)andω(G)to denote the chromatic number and clique number of G respectively.A P_(5)is a path on 5 vertices,and an HVN is a K_(4)together with one more vertex which is adjacent to exactly two...Let G be a graph.We useχ(G)andω(G)to denote the chromatic number and clique number of G respectively.A P_(5)is a path on 5 vertices,and an HVN is a K_(4)together with one more vertex which is adjacent to exactly two vertices of K_(4).Combining with some known result,in this paper we show that if G is(P_(5),HVN)-free,thenχ(G)≤max{min{16,ω(G)+3},ω(G)+1}.This upper bound is almost sharp.展开更多
基金supported by the National Natural Science Foundation of China(No.12101117)Natural Science Foundation of Jiangsu Province(No.BK20200344)。
文摘Let G be a graph.We useχ(G)andω(G)to denote the chromatic number and clique number of G respectively.A P_(5)is a path on 5 vertices,and an HVN is a K_(4)together with one more vertex which is adjacent to exactly two vertices of K_(4).Combining with some known result,in this paper we show that if G is(P_(5),HVN)-free,thenχ(G)≤max{min{16,ω(G)+3},ω(G)+1}.This upper bound is almost sharp.
