Zdenek Dvorak

A graph drawn in a surface is a k-near-quadrangulation if the product of the lengths of its faces, except for 4-faces, is at most k. Near-quadrangulations play a fundamental role in the theory of 3-colorability of triangle-free graphs on surfaces. We...

Summary: Recently, Grohe and Marx proved that for every H, there exist constants k, D and t such that if G does not contain H as a topologicalminor, then G is a clique sum of graphs that either avoid K_k as a minoror contain at most t vertices of...