CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt170",{id:"formSmash:upper:j_idt170",widgetVar:"widget_formSmash_upper_j_idt170",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt178_j_idt181",{id:"formSmash:upper:j_idt178:j_idt181",widgetVar:"widget_formSmash_upper_j_idt178_j_idt181",target:"formSmash:upper:j_idt178:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

A characterization of panconnected graphs satisfying a local ore-type conditionPrimeFaces.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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1996 (English)In: Journal of Graph Theory, ISSN 0364-9024, E-ISSN 1097-0118, Vol. 22, no 2, p. 95-103Article in journal (Refereed) Published
##### Abstract [en]

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

Wiley Subscription Services, Inc., A Wiley Company , 1996. Vol. 22, no 2, p. 95-103
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:liu:diva-143770DOI: 10.1002/(SICI)1097-0118(199606)22:2<95::AID-JGT1>3.0.CO;2-FOAI: oai:DiVA.org:liu-143770DiVA, id: diva2:1166935
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt825",{id:"formSmash:j_idt825",widgetVar:"widget_formSmash_j_idt825",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt837",{id:"formSmash:j_idt837",widgetVar:"widget_formSmash_j_idt837",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt852",{id:"formSmash:j_idt852",widgetVar:"widget_formSmash_j_idt852",multiple:true}); Available from: 2017-12-17 Created: 2017-12-17 Last updated: 2017-12-17Bibliographically approved

It is well known that a graph G of order p ≥ 3 is Hamilton-connected if d(u) + d(v) ≥ p + 1 for each pair of nonadjacent vertices u and v. In this paper we consider connected graphs G of order at least 3 for which d(u) + d(v) ≥ |N(u) ∪ N(v) ∪ N(w)| + 1 for any path uwv with uv ∉ E(G), where N(x) denote the neighborhood of a vertex x. We prove that a graph G satisfying this condition has the following properties: (a) For each pair of nonadjacent vertices x, y of G and for each integer k, d(x, y) ≤ k ≤ |V(G)| − 1, there is an x − y path of length k. (b) For each edge xy of G and for each integer k (excepting maybe one k η 3,4) there is a cycle of length k containing xy.Consequently G is panconnected (and also edge pancyclic) if and only if each edge of G belongs to a triangle and a quadrangle.Our results imply some results of Williamson, Faudree, and Schelp. © 1996 John Wiley & Sons, Inc.

doi
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CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1931",{id:"formSmash:lower:j_idt1931",widgetVar:"widget_formSmash_lower_j_idt1931",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1932_j_idt1934",{id:"formSmash:lower:j_idt1932:j_idt1934",widgetVar:"widget_formSmash_lower_j_idt1932_j_idt1934",target:"formSmash:lower:j_idt1932:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});