The extremal function for 3-linked graphs

Authors:
Robin Thomas;Paul Wollan
Affiliations:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA;School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
Venue:
Journal of Combinatorial Theory Series B
Year:
2008

Citing 6
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Abstract

A graph is k-linked if for every set of 2k distinct vertices {s"1,...,s"k,t"1,...,t"k} there exist disjoint paths P"1,...,P"k such that the endpoints of P"i are s"i and t"i. We prove every 6-connected graph on n vertices with 5n-14 edges is 3-linked. This is optimal, in that there exist 6-connected graphs on n vertices with 5n-15 edges that are not 3-linked for arbitrarily large values of n.