Vol. 55, No. 2, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 332: 1
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Quotients of complete graphs: revisiting the Heawood map-coloring problem

Jonathan Light Gross and Thomas William Tucker

Vol. 55 (1974), No. 2, 391–402
Abstract

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
Milestones
Received: 2 May 1974
Published: 1 December 1974
Authors
Jonathan Light Gross
http://www.cs.columbia.edu/~gross
Thomas William Tucker
Colgate University
NY
United States
http://www.colgate.edu/DesktopDefault1.aspx?tabid=684\&pgID=3400\&fID=202