On circuits and pancyclic line graphs

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Benhocine, A. and Clark, L. and Köhler, N. and Veldman, H.J. (1986) On circuits and pancyclic line graphs. Journal of Graph Theory, 10 (3). pp. 411-425. ISSN 0364-9024

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Abstract:Clark proved that L(G) is hamiltonian if G is a connected graph of order n ≥ 6 such that deg u + deg v ≥ n - 1 - p(n) for every edge uv of G, where p(n) = 0 if n is even and p(n) = 1 if n is odd. Here it is shown that the bound n - 1 - p(n) can be decreased to (2n + 1)/3 if every bridge of G is incident with a vertex of degree 1, which is a necessary condition for hamiltonicity of L(G). Moreover, the conclusion that L(G) is hamiltonian can be strengthened to the conclusion that L(G) is pancyclic. Lesniak-Foster and Williamson proved that G contains a spanning closed trail if |V(G)| = n ≥ 6, δ(G) 2 and deg u + deg v ≥ n - 1 for every pair of nonadjacent vertices u and v. The bound n - 1 can be decreased to (2n + 3)/3 if G is connected and bridgeless, which is necessary for G to have a spanning closed trail.
Item Type:Article
Copyright:© 1986 Wiley InterScience
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/70813
Official URL:http://dx.doi.org/10.1002/jgt.3190100317
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