Generating Closed 2-Cell Embeddings in the Torus and the Projective Plane.
We prove that under appropriate assumptions adding or removing an infinite amount of edges to a given planar graph preserves its non-hyperbolicity, a result which is shown to be false in general. In particular, we make a conjecture that every tessellation graph of ℝ2 with convex tiles is non-hyperbolic; it is shown that in order to prove this conjecture it suffices to consider tessellation graphs of ℝ2 such that every tile is a triangle and a partial answer to this question is given. A weaker version...
A 2-stratified graph is a graph whose vertex set has been partitioned into two subsets, called the strata or color classes of . Two -stratified graphs and are isomorphic if there exists a color-preserving isomorphism from to . A -stratified graph is said to be homogeneously embedded in a -stratified graph if for every vertex of and every vertex of , where and are colored the same, there exists an induced -stratified subgraph of containing and a color-preserving...