Title

Highly linked graphs

Abstract

A graph with at least 2k vertices is said to be k-linked if, for any choice s1, . . . ,sk, t1, . . . ,tk. of 2k distinct vertices there are vertex disjoint paths P1, . . . ,Pk with Pi joining si to ti, 1≤i≤k. Recently Robertson and Seymour [16] showed that a graph G is k-linked provided its vertex connectivity k(G) exceeds 10k-√log2 k. We show here that k(G)≥22k will do.

Publication Title

Combinatorica

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