English

Hamiltonicity of doubly semi-equivelar maps on the torus

Combinatorics 2021-10-19 v2 Geometric Topology

Abstract

The well-known twenty types of 2-uniform tilings of the plane give rise infinitely many doubly semi-equivelar maps on the torus. In this article, we show that every such doubly semi-equivelar map on the torus contains a Hamiltonian cycle. As a consequence, we establish the Nash-Williams conjecture for the graphs associated with these doubly semi-equivelar maps by showing that these graphs are either 3-connected or 4-connected.

Keywords

Cite

@article{arxiv.2101.02541,
  title  = {Hamiltonicity of doubly semi-equivelar maps on the torus},
  author = {Yogendra Singh and Anand Kumar Tiwari and Seema Kushwaha},
  journal= {arXiv preprint arXiv:2101.02541},
  year   = {2021}
}

Comments

19. arXiv admin note: text overlap with arXiv:2005.00332