Line graphs of multigraphs and Hamilton-connectedness of claw-free graphs

Abstract

We introduce a closure concept that turns a claw-free graph into the line graph of a multigraph while preserving its (non-)Hamiltonconnectedness. As an application, we show that every 7-connected claw-free graph is Hamilton-connected, and we show that the wellknown conjecture by Matthews and Sumner (every 4-connected clawfree graph is hamiltonian) is… (More)
DOI: 10.1002/jgt.20498

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Cite this paper

@article{Ryjcek2011LineGO, title={Line graphs of multigraphs and Hamilton-connectedness of claw-free graphs}, author={Zdenek Ryj{\'a}cek and Petr Vr{\'a}na}, journal={Journal of Graph Theory}, year={2011}, volume={66}, pages={152-173} }