Lattice graphs with non-concurrent longest cycles

No hypohamiltonian graphs are embeddable in the planar square lattice. This lattice contains, however, graphs in which every vertex is missed by some longest cycle. In this paper we present graphs with this property, embeddable in various lattices, and of remarkably small order.

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Bibliographic Details
Published inRendiconti - Seminario matematico della Università di Padova Vol. 132; pp. 75 - 82
Main Authors Jumani, Ali Dino, Zamfirescu, Carol, Zamfirescu, Tudor
Format Journal Article
LanguageEnglish
Published Zuerich, Switzerland European Mathematical Society Publishing House 01.01.2014
Subjects
Combinatorics
Lattice graphs
longest cycles
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Summary:No hypohamiltonian graphs are embeddable in the planar square lattice. This lattice contains, however, graphs in which every vertex is missed by some longest cycle. In this paper we present graphs with this property, embeddable in various lattices, and of remarkably small order.
ISSN:0041-8994
2240-2926
DOI:10.4171/RSMUP/132-6