On the Hamiltonian Number of a Planar Graph
Combinatorics
2015-08-28 v1
Abstract
The Hamiltonian number of a connected graph is the minimum of the lengths of the closed, spanning walks in the graph. In 1968, Grinberg published a necessary condition for the existence of a Hamiltonian cycle in a planar graph, formulated in terms of the lengths of its face cycles. We show how Grinberg's theorem can be adapted to provide a lower bound on the Hamiltonian number of a planar graph.
Cite
@article{arxiv.1508.06892,
title = {On the Hamiltonian Number of a Planar Graph},
author = {Thomas M. Lewis},
journal= {arXiv preprint arXiv:1508.06892},
year = {2015}
}
Comments
11 pages