Hamiltonian circuits in some maps on the torus

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


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
Issue number4
StatePublished - 1 Jan 1972
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Hamiltonian circuits in some maps on the torus'. Together they form a unique fingerprint.

Cite this