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Fan-type theorem for path-connectivity. (English) Zbl 1002.05041
Let \(\mu(G)\) be \(\min\{\max\{d_G(u), d_G(v)\}\mid\text{distance}(u,v)= 2\}\) for a connected noncomplete graph \(G\). The authors prove that for each 3-connected noncomplete graph \(G\) each pair of distinct vertices is joined by a path of length at least \(\min\{|V(G)|- 1, 2\mu(G)- 2\}\). This proves also a conjecture of H. Enomoto, K. Hirohata and K. Ota [J. Graph Theory 24, 275-279 (1997; Zbl 0868.05033)].
Reviewer: M.Hager (Leonberg)

MSC:
05C40 Connectivity
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