Hamiltonian circuits in some maps on the torus

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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.

Original languageEnglish
Pages (from-to)299-314
Number of pages16
JournalDiscrete Mathematics
Volume1
Issue number4
DOIs
StatePublished - 1 Jan 1972
Externally publishedYes

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