4-连通、高次、1-坚韧图的周长

Circumference of 4-Connected Tough Graphs with High Order

通过研究4-连通、1-坚韧图中控制圈,给出了4-连通、高次、1-坚韧图周长的下界.设G为4-连通、1-坚韧的n阶图,n≥20且σ5(G)≥n+C(G)-1,则有C(G)≥min{n,n+σ5(G)5-α(G)}.

By studying dominating cycles in 4-Connected Tough graphs, the lower bound of circumferences in 4-Connected Tough graphs is given. Let G be a 4-Connected Tough graphs of order n,if n≥20and σ5（G）≥n＋C（G）-1,then C（G）≥min{n,n＋σ（G）/5-α（G）}.