A novel condition for Hamiltonicity; Constructing Hamiltonian circuits

Abstract

In this paper, we derive a new necessary and sufficient condition for a simple, undirected graph to have a Hamiltonian circuit. Our novel approach uses a modified incidence matrix and constructs Hamiltonian circuits from the graph's spanning trees. We furthermore optimise the underlying spanning-tree algorithm, and give an example of our results. © 2011 IEEE.