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Hamiltonian paths and hamiltonian connectivity in graphs

✍ Scribed by Bing Wei

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 388 KB
Volume: 121
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90555-8

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✦ Synopsis

Let G be a 2-connected graph with n vertices such that d(u)+d(u)+d(w)-IN(u)nN(u)nN(w)I

an+ 1 holds for any triple of independent vertices u, v and w. Then for any distinct vertices u and u such that {u, 0) is not a cut vertex set of G, there is a hamiltonian path between u and o. In particular, if G is 3-connected, then G is hamiltonian-connected. This is closely related to the main result in Flandrin et al. (1991) and generalizes a theorem of Ore ( ) and a theorem of .

tonian path (H-path for short) between any two distinct vertices of G.

Recently, Flandrin et al.

[2] proved the following result.

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