liu.seSearch for publications in DiVA
Change search

Cite
Citation style
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• oxford
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf
A characterization of panconnected graphs satisfying a local ore-type condition
Department of Mathematics, University of Umeå, Umeå, Sweden / Department of Mathematical Cybernetics, Yerevan State University, Yerevan, Republic of Armenia.
Department of Mathematics, University of Umeå, Umeå, Sweden.
Department of Mathematical Cybernetics, Yerevan State University, Yerevan, Republic of Armenia.
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]

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.

Place, publisher, year, edition, pages
Wiley Subscription Services, Inc., A Wiley Company , 1996. Vol. 22, no 2, p. 95-103
Mathematics
Identifiers
OAI: oai:DiVA.org:liu-143770DiVA, id: diva2:1166935
Available from: 2017-12-17 Created: 2017-12-17 Last updated: 2017-12-17Bibliographically approved

Open Access in DiVA

A characterization of panconnected graphs satisfying a local ore-type condition(583 kB)89 downloads
File information
File name FULLTEXT01.pdfFile size 583 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Publisher's full text

Authority records BETA

Asratian, Armen S.

Search in DiVA

By author/editor
Asratian, Armen S.
In the same journal
Journal of Graph Theory
Mathematics

Search outside of DiVA

The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available
doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 2329 hits

Cite
Citation style
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• oxford
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf