Hourglasses and Hamilton cycles in 4-connected claw-free graphs

We show that if G is a 4‐connected claw‐free graph in which every induced hourglass subgraph S contains two non‐adjacent vertices with a common neighbor outside S, then G is hamiltonian. This extends the fact that 4‐connected claw‐free, hourglass‐free graphs are hamiltonian, thus proving a broader s...

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Bibliographic Details
Published inJournal of graph theory Vol. 48; no. 4; pp. 267 - 276
Main Authors Kaiser, Tomáš, Li, MingChu, Ryjáček, Zdeněk, Xiong, Liming
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.04.2005
Subjects
claw-free graph
closure
Hamilton cycle
hourglass
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Summary:We show that if G is a 4‐connected claw‐free graph in which every induced hourglass subgraph S contains two non‐adjacent vertices with a common neighbor outside S, then G is hamiltonian. This extends the fact that 4‐connected claw‐free, hourglass‐free graphs are hamiltonian, thus proving a broader special case of a conjecture by Matthews and Sumner. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 267–276, 2005
Bibliography:Fund of LiuHui Applied Mathematics Research - No. T23 (to M. L.)
istex:B66F74F2F08E853FBA62A678AA8EB50A673FA71E
Fund of Basic Research of Beijing Institute of Technology (to L. X.)
Nature Science Fund of China (to M. L.)
ark:/67375/WNG-KMLD358D-D
ArticleID:JGT20056
Fund of Natural Science of Jiangxi Province (to L. X.)
Czech Ministry of Education - No. ME 418 (to T. K. and Z. R.); No. LN00A056 (to T. K. and Z. R.)
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.20056