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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.
05C38 Paths and cycles
05C40 Connectivity
Full Text: DOI
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