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New local conditions for a graph to be hamiltonianPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2006 (English)In: Graphs and Combinatorics, ISSN 0911-0119, Vol. 22, no 2, 153-160 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2006. Vol. 22, no 2, 153-160 p.
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:liu:diva-36332DOI: 10.1007/s00373-006-0646-3Local ID: 31006OAI: oai:DiVA.org:liu-36332DiVA: diva2:257180
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Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2011-01-11

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.

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