k(≥3)连通偶图的周长

On the Length of Perimeter of k(≥3)-Connected Bipartite Graphs

设 G(A1 ,A2 ,E)为 k( 3 )连通偶图 ,(A1 ,A2 )为 G的顶点二分划 ,δ=min{ d(x) |x∈V(G) } ,则 G的周长至少为 2 min{ |A1 |,|A2 |,2 δ- 1 }(δ图除外 ) 。

Let G(A 1,A 2)be a k(3)-Connected bipartite graph with bipastition ( A 1,A 2),δ =min {d(x)|x∈V(G) },then G contains a length of perimeter at least 2min{ |A 1|,|A 2|,2δ-1}(δ graph excepted)