A note on Hamiltonian cycles in planar graphs

Abstract

Unlike the problem of finding Eulerian cycles, the problem of deciding whether a given graph has a Hamiltonian cycle is NP-complete, even when restricting to planar graphs. There are however some criteria that can be used in special cases. One of them can be derived by Grinberg’s theorem. In this note, we give some more (slightly more general) criteria derived from Grinberg’s theorem to show that a graph does not have a Hamiltonian cycle.