On the Hamiltonian number of a planar graph

Thomas M. Lewis
2018 Discussiones Mathematicae Graph Theory  
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 plane graph, formulated in terms of the degrees of its faces. We show how Grinberg's theorem can be adapted to provide a lower bound on the Hamiltonian number of a plane graph.
doi:10.7151/dmgt.2084 fatcat:awwerii2cfhyniiuegpwcjtmfe