3-γ-临界图 G中关于 i(G) =γ(G)的一个充分条件

A Sufficient Condition on I(G)=γ(G) for 3-γ-critical Graph

如果图 G满足γ( G) =k且对图 G中任两个不相邻的点 x,y有γ( G +xy) =k- 1 ,则称图 G为 k-γ-临界图 ,如果图 G满足γ( G) =k且对图 G中任何距离为 d的两点 x,y有γ( G +xy) =k - 1 ,则称图 G为 k - (γ,d) -临界图 .Sumner和 Blitch猜想在 3-γ-临界图中有γ( G) =i( G) .Oellermann和 Swart猜想 3- (γ,2 ) -临界图中有γ( G) =i( G) ,这篇文章中我们提出 3-γ-临界图中使γ( G) =i( G)

Sumner and Blitch defined a graph G to be k γ critical if γ(G)=k and γ(G+uv)=k-1 for each pair u,v of nonadjacent vertices of G. And conjecture that γ(G)=i(G) for 3 γ critical graph. Henning Oellermann and Swart defined a graph to be k (γ,d) critical if γ(G)=k and γ(G+uv)=k-1 for each pair u,v of nonadjacent vertices of G that are at distance at most d apart. And conjecture: if G is a connected 3 (γ,2) critical graph, then γ(G)=i(G). In this paper we prove that a sufficient condition on γ(G)=i(G) for 3 γ critical graph.