Pairs of Hamiltonian circuits in 5-connected planar graphs

Joseph Zaks

doi:10.1016/0095-8956(76)90051-4

Pairs of Hamiltonian circuits in 5-connected planar graphs

Joseph Zaks

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Settling a problem raised by B. Grünbaum, J. Malkevitch, and the author, we present 5-valent 5-connected planar graphs that admit no pairs of edgedisjoint Hamiltonian circuits; our smallest example has 176 vertices. This is used to construct an infinite family of 5-valent 5-connected planar graphs, in which every member has the property that any pair of Hamiltonian circuits in it share at least about 1 168 of their edges. We construct 4- and 5-valent, 3-connected non-Hamiltonian planar graphs.

Original language	English
Pages (from-to)	116-131
Number of pages	16
Journal	Journal of Combinatorial Theory. Series B
Volume	21
Issue number	2
DOIs	https://doi.org/10.1016/0095-8956(76)90051-4
State	Published - Oct 1976

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/0095-8956(76)90051-4

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abstract = "Settling a problem raised by B. Gr{\"u}nbaum, J. Malkevitch, and the author, we present 5-valent 5-connected planar graphs that admit no pairs of edgedisjoint Hamiltonian circuits; our smallest example has 176 vertices. This is used to construct an infinite family of 5-valent 5-connected planar graphs, in which every member has the property that any pair of Hamiltonian circuits in it share at least about 1 168 of their edges. We construct 4- and 5-valent, 3-connected non-Hamiltonian planar graphs.",

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AB - Settling a problem raised by B. Grünbaum, J. Malkevitch, and the author, we present 5-valent 5-connected planar graphs that admit no pairs of edgedisjoint Hamiltonian circuits; our smallest example has 176 vertices. This is used to construct an infinite family of 5-valent 5-connected planar graphs, in which every member has the property that any pair of Hamiltonian circuits in it share at least about 1 168 of their edges. We construct 4- and 5-valent, 3-connected non-Hamiltonian planar graphs.

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Pairs of Hamiltonian circuits in 5-connected planar graphs

Abstract

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