Hamiltonian circuits in some maps on the torus

Amos Altshuler

doi:10.1016/0012-365X(72)90037-4

Hamiltonian circuits in some maps on the torus

Amos Altshuler

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

46 Scopus citations

Abstract

A map on the torus is called regular of type {p, q}, if each vertex is of valence q and each face has p edges. It is proved that in the graph consisting of the vertices and edges of a regular map on the torus of type {3, 6} or {4, 4} there exists a Hamiltonian circuit. For maps of type {6, 3} the same problem is only partially solved. A Hamiltonian circuit is also shown to exist in every 6-connected graph on the torus.

Original language	English
Pages (from-to)	299-314
Number of pages	16
Journal	Discrete Mathematics
Volume	1
Issue number	4
DOIs	https://doi.org/10.1016/0012-365X(72)90037-4
State	Published - 1 Jan 1972
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(72)90037-4

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abstract = "A map on the torus is called regular of type {p, q}, if each vertex is of valence q and each face has p edges. It is proved that in the graph consisting of the vertices and edges of a regular map on the torus of type {3, 6} or {4, 4} there exists a Hamiltonian circuit. For maps of type {6, 3} the same problem is only partially solved. A Hamiltonian circuit is also shown to exist in every 6-connected graph on the torus.",

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AB - A map on the torus is called regular of type {p, q}, if each vertex is of valence q and each face has p edges. It is proved that in the graph consisting of the vertices and edges of a regular map on the torus of type {3, 6} or {4, 4} there exists a Hamiltonian circuit. For maps of type {6, 3} the same problem is only partially solved. A Hamiltonian circuit is also shown to exist in every 6-connected graph on the torus.

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Hamiltonian circuits in some maps on the torus

Abstract

ASJC Scopus subject areas

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