Vol. 55, No. 2, 1974

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Quotients of complete graphs: revisiting the Heawood map-coloring problem

Jonathan Light Gross and Thomas William Tucker

Vol. 55 (1974), No. 2, 391–402

The principal result of this paper is the determination of every graph that can be covered by a complete graph. It is shown that for every odd divisor d of the number n of vertices of a complete graph Kn, there is a unique graph with n∕d vertices covered by Kn, and that there are no other graphs covered by Kn. This determination is applied to an examination of certain aspects of the solution to the Heawood map-coloring problem. In particular, combinatorial arguments of the solution are set in a topological framework of branched covering spaces.

Mathematical Subject Classification 2000
Primary: 05C10
Received: 2 May 1974
Published: 1 December 1974
Jonathan Light Gross
Thomas William Tucker
Colgate University
United States