Some recent results in topological graph theory

Abstract

This paper examines a number of recent results in topological graph theory. Invariants such as genus, thickness, skewness, crossing number, and local crossing number are introduced and related to one another. We then deal with topological techniques in the theory of chromatic numbers, and state a very ambitious meta-conjecture which is quite useful in generating true theorems. In closing, we attempt to suggest appropriate directions for further research in topological graph theory, and we give a few results to indicate the richness of the terrain.KeywordsProjective PlanePlanar GraphChromatic NumberCombinatorial TheoryComplete Bipartite GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.