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On the local nature of some classical theorems on Hamilton cycles
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
2007 (English)In: Australasian journal of combinatorics, ISSN 1034-4942, Vol. 38, 77-86 p.Article in journal (Refereed) Published
Abstract [en]

The following result gives a flavour of what is in this paper. Ore's theorem is that if $d(u)+d(v)\ge|G|$ for all non-adjacent $u,v\in G$ then $G$ is Hamiltonian. The authors show that this is equivalent to specifying that $d(u)+d(v)\ge |B(x)|$ for every $x\in G$ and all non-adjacent $u,v\in B(x)$, where $B(x)$ is the ball of radius three centred at $x$. The reason is that the condition implies $G$ has diameter at most two, and so $B(x)=G$.

Place, publisher, year, edition, pages
2007. Vol. 38, 77-86 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-36335Local ID: 31010OAI: oai:DiVA.org:liu-36335DiVA: diva2:257183
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2010-04-13

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