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

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Broersma, H.J. and Veldman, H.J. (1987) 3-Connected line graphs of triangular graphs are panconnected and 1-hamiltonian. Journal of Graph Theory, 11 (3). pp. 399-407. ISSN 0364-9024

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Abstract: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.
Item Type:Article
Copyright:© 1987 Wiley InterScience
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/70828
Official URL:http://dx.doi.org/10.1002/jgt.3190110314
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