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On n-Hamiltonian line graphs

โœ Scribed by Linda Lesniak-Foster


Book ID
103502637
Publisher
Elsevier Science
Year
1977
Tongue
English
Weight
853 KB
Volume
22
Category
Article
ISSN
0095-8956

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๐Ÿ“œ SIMILAR VOLUMES


On hamiltonian line graphs
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## Abstract Sufficient conditions on the degrees of a graph are given in order that its line graph have a hamiltonian cycle.

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A well-known conjecture of Thomassen says that every 4-connected line graph is hamiltonian. In this paper we prove that every 7-connected line graph is hamiltonian-connected. For line graph, C. Thomassen [l] made the following conjecture. Conjecture. Every 4-connected line graph is hamiltonian.

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## An extension of CI theorem of Chamhnd and Wall is obtained and, with it, a bound on the lamiltoniau index h(G) of a connected graph G (other than a path) is determined. As a tonsequence, it is Fhown that if G is homogeneously traceable, then h(Gj ~2.