Graphs of Maps

Abstract

This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as planar abstract duality, and is characterized topologically. An extension of the Gauss code problem treating together the cases in which the surface involved is the plane or the real projective plane is established. The problem of finding a minimum transversal of orientation-reversing circuits in graphs on arbitrary surfaces is proved to be NP-complete and is algorithmically solved for the special case where the surface is the real projective plane.