Every graph occurs as an induced subgraph of some hypohamiltonian graph

We prove the titular statement. This settles a problem of Chvátal from 1973 and encompasses earlier results of Thomassen, who showed it for K3, and Collier and Schmeichel, who proved it for bipartite graphs. We also show that for every outerplanar graph there exists a planar hypohamiltonian graph co...

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Bibliographic Details
Published inJournal of graph theory Vol. 88; no. 4; pp. 551 - 557
Main Authors Zamfirescu, Carol T., Zamfirescu, Tudor I.
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc 01.08.2018
Subjects
05C10
05C45
05C60
hypohamiltonian
induced subgraph
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Summary:We prove the titular statement. This settles a problem of Chvátal from 1973 and encompasses earlier results of Thomassen, who showed it for K3, and Collier and Schmeichel, who proved it for bipartite graphs. We also show that for every outerplanar graph there exists a planar hypohamiltonian graph containing it as an induced subgraph.
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.22228