Hamiltonian Cycles in Triangular Grids

We study the Hamiltonian Cycle problem in graphs induced by subsets of the vertices of the tiling of the plane with equilateral triangles. By analogy with grid graphs we call such graphs triangular grid graphs. Following the analogy, we define the class of solid triangular grid graphs. We prove that the Hamiltonian Cycle problem is NPcomplete for triangular grid graphs. We show that with the exception of the "Star of David", a solid triangular grid graph without cut vertices is always Hamiltonian.

• Type: Conference
• Year: 2006
• Where: CCCG
• Authors: Valentin Polishchuk, Esther M. Arkin, Joseph S. B. Mitchell
• Keywords: CCCG 2006, CCCG 2007, Hamiltonian Cycle Problem, Solid Triangular Grid, Triangular Grid Graph