Highly linked graphs

Abstract

A graph with at least 2k vertices is said to bek-linked if, for any choices 1,...,s k ,t 1,...,t k of 2k distinct vertices there are vertex disjoint pathsP 1,...,P k withP i joinings i tot i , 1≤ik. Recently Robertson and Seymour [16] showed that a graphG isk-linked provided its vertex connectivityk(G) exceeds\(10k\sqrt {\log _2 k}\). We show here thatk(G)≥22k will do.

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Bollobás, B., Thomason, A. Highly linked graphs. Combinatorica 16, 313–320 (1996). https://doi.org/10.1007/BF01261316

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Mathematics Subject Classification (1991)

  • 05 C 40
  • 05 C 38