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On Hamiltonian paths in distance graphs

✍ Scribed by Christian Löwenstein; Dieter Rautenbach; Friedrich Regen


Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
270 KB
Volume
24
Category
Article
ISSN
0893-9659

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📜 SIMILAR VOLUMES


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## 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,

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## Abstract Let __G__ be a graph of order __n__. We show that if __G__ is a 2‐connected graph and max{__d(u), d(v)__} + |__N(u)__ U __N(v)__| ≥ __n__ for each pair of vertices __u, v__ at distance two, then either __G__ is hamiltonian or G 3K~n/3~ U T~1~ U T~2~, where n  O (mod 3), and __T__~1~ a