重子图条件下图的坚韧性

Results on toughness in graphs under heavy subgraph conditions

设G是一个有限的无向简单图,研究了图G在重子图条件下的坚韧性.在对低连通图坚韧性研究的基础上,通过分析图的结构,刻画了k-连通图是τ(τ≤1)-坚韧的重子图条件的特点,给出了k-连通-S重图是τ(τ≤1)-坚韧的充要条件,进一步推广了对图的坚韧性的研究.

Let G be a graph on n vertices. The toughness of graphs under special heavy subgraph condi- tions is studied in the paper. On the basis of studying the toughness of the low connective graphs, the graph S was characterized such that every k- connected S-heavy graph was r-tough and gave the necessa- ry and sufficient conditions,which promotes the research of the toughness of graphs.