Hexagonal Tilings and Locally C6 Graphs

Abstract

We give a complete classification of hexagonal tilings and locally C6 graphs, by showing that each of them has a natural embedding in the torus or in the Klein bottle (see [12]). We also show that locally grid graphs, defined in [9, 12], are minors of hexagonal tilings (and by duality of locally C6 graphs) by contraction of a particular perfect matching and deletion of the resulting parallel edges, in a form suitable for the study of their Tutte uniqueness