Hamiltonicity of Topological Grid Graphs

Christina Zamfirescu (City University of New York, USA)

Tudor Zamfirescu (Universität Dortmund, Germany)

Abstract: In this paper we study connectivity and hamiltonicity properties of the topological grid graphs, which are a natural type of planar graphs associated with finite subgraphs of the usual square lattice graph of the plane. The main results are as follows. The shortness coefficient of the family of all topological grid graphs is at most 16/17. Every 3-connected topological grid graph is hamiltonian.

Keywords: 3-connectedness, grid graph, hamiltonian graph, shortness coefficient, topological grid graph

Categories: G.2.2