Affordable Access

Criticality of counterexamples to toroidal edge-hamiltonicity

Authors
Type
Preprint
Publication Date
Submission Date
Identifiers
arXiv ID: 1312.1379
Source
arXiv
License
Yellow
External links

Abstract

A well-known conjecture of Gr\"unbaum and Nash-Williams proposes that 4-connected toroidal graphs are hamiltonian. The corresponding results for 4-connected planar and projective-planar graphs were proved by Tutte and by Thomas and Yu, respectively, using induction arguments that proved a stronger result, that every edge is on a hamilton cycle. However, this stronger property does not hold for 4-connected toroidal graphs: Thomassen constructed counterexamples. Thus, the standard inductive approach will not work for the torus. One possible way to modify it is by characterizing the situations where some edge is not on a hamilton cycle. We provide a contribution in this direction, by showing that the obvious generalizations of Thomassen's counterexamples are critical in a certain sense.

Statistics

Seen <100 times