The combinatorial map color theorem

Abstract

Abstract This paper is written in the spirit of the author's book: Map Color Theorem (1974). We try to develop the Map Color Theorem in a combinatorial way, circumventing the unwieldy embedding theory. Similar (but not identical) generalizations have recently and independently been developed by Alpert (in press) and by Stahl (in press). The first nine theorems are one‐dimensional versions of known facts from the theory of two‐dimensional compact manifolds. Theorems 10 to 13 are to my knowledge completely new results.