Abstract
Chartrand and Pippert 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.
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This research was partly done on a visit to the Institute of Systems Science of Academia Sinica (Beijing, China) under the project ME 418 of the Czech Ministery of Education. These authors are partly supported by the project LN00A056 of the Czech Ministery of Education.
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Chen, C., Čada, R., Kaiser, T. et al. Short Disjoint Paths in Locally Connected Graphs. Graphs and Combinatorics 23, 509–519 (2007). https://doi.org/10.1007/s00373-007-0754-8
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DOI: https://doi.org/10.1007/s00373-007-0754-8