Abstract
In 1985 P. M. Winkler (Emory) conjectured that every connected graph G contains a vertex k, such that the removal of k and all incident edges enlarges the average distance between vertices of G by at most the factor 4 3 . We show that every l-connected graph has a vertex whose removal increases the average distance in the graph by no more than a factor of l (l−1) . This proves Winkler's conjecture for 4-connected graphs.
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