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Short disjoint paths in locally connected graphs. (English) Zbl 1127.05056
Summary: G. Chartrand and R. E. Pippert [Cas. Pest. Mat. 99, 158–163 (1974; Zbl 0278.05113)] proved that a connected, locally \(k\)-connected graph is \((k + 1)\)-connected. We investigate the lengths of \(k + 1\) disjoint paths between two vertices in locally \(k\)-connected graphs with respect to several graph parameters, e.g. the \(k\)-diameter of a graph. We also give a generalization of the mentioned result.
MSC:
05C38 Paths and cycles
05C40 Connectivity
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References:
[1] Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications, Macmillan, London, 1976
[2] Chartrand, G., Pippert, R.E.: Locally connected graphs, Časopis pro pěstování matematiky, 99, 158–163 (1974) · Zbl 0278.05113
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