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Gromov hyperbolicity of planar graphs

Alicia Cantón, Ana Granados, Domingo Pestana, José Rodríguez (2013)

Open Mathematics

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...

Homogeneously embedding stratified graphs in stratified graphs

Gary Chartrand, Donald W. Vanderjagt, Ping Zhang (2005)

Mathematica Bohemica

A 2-stratified graph G is a graph whose vertex set has been partitioned into two subsets, called the strata or color classes of G . Two 2 -stratified graphs G and H are isomorphic if there exists a color-preserving isomorphism φ from G to H . A 2 -stratified graph G is said to be homogeneously embedded in a 2 -stratified graph H if for every vertex x of G and every vertex y of H , where x and y are colored the same, there exists an induced 2 -stratified subgraph H ' of H containing y and a color-preserving...

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