3-Connected line graphs of triangular graphs are panconnected and 1-hamiltonian

Haitze J. Broersma, H.J. Veldman

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A graph is k-triangular if each edge is in at least k triangles. Triangular is a synonym for 1-triangular. It is shown that the line graph of a triangular graph of order at least 4 is panconnected if and only if it is 3-connected. Furthermore, the line graph of a k-triangular graph is k-hamiltonian if and only if it is (k + 2)-connected (k ≥ 1). These results generalize work of Clark and Wormald and of Lesniak-Foster. Related results are due to Oberly and Sumner and to Kanetkar and Rao.
Original languageUndefined
Pages (from-to)399-407
JournalJournal of graph theory
Issue number3
Publication statusPublished - 1987


  • IR-70828

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