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The combinatorial map color theorem
Author(s) -
Ringel Gerhard
Publication year - 1977
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190010210
Subject(s) - mathematics , embedding , combinatorics , discrete mathematics , computer science , artificial intelligence
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.