The Extremal Function for 3-linked Graphs


A graph is k-linked if for every set of 2k distinct vertices {s1,..., sk, t1,..., tk} there exist disjoint paths P1,..., Pk such that the endpoints of Pi are si and ti. We prove every 6-connected graph on n vertices with 5n βˆ’ 14 edges is 3-linked. This is optimal, in that there exist 6-connected graphs on n vertices with 5n βˆ’ 15 edges that are not 3-linked for arbitrarily large values of n

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Last time updated on 22/10/2014

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