New local conditions for a graph to be hamiltonian
2006 (English)In: Graphs and Combinatorics, ISSN 0911-0119, Vol. 22, no 2, 153-160 p.Article in journal (Refereed) Published
For a vertex w of a graph G the ball of radius 2 centered at w is the subgraph of G induced by the set M 2(w) of all vertices whose distance from w does not exceed 2. We prove the following theorem: Let G be a connected graph where every ball of radius 2 is 2-connected and d(u)+d(v)|M 2(w)|-1 for every induced path uwv. Then either G is hamiltonian or [InlineMediaObject not available: see fulltext.] for some p2 where denotes join. As a corollary we obtain the following local analogue of a theorem of Nash-Williams: A connected r-regular graph G is hamiltonian if every ball of radius 2 is 2-connected and [InlineMediaObject not available: see fulltext.] for each vertex w of G. © Springer-Verlag 2006.
Place, publisher, year, edition, pages
2006. Vol. 22, no 2, 153-160 p.
IdentifiersURN: urn:nbn:se:liu:diva-36332DOI: 10.1007/s00373-006-0646-3Local ID: 31006OAI: oai:DiVA.org:liu-36332DiVA: diva2:257180