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Submap Density and Asymmetry Results for Two Parameter Map Families

Published online by Cambridge University Press:  01 March 1997

EDWARD A. BENDER
Affiliation:
Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA
E. RODNEY CANFIELD
Affiliation:
Department of Computer Science, University of Georgia, Athens, GA 30602, USA
ZHICHENG GAO
Affiliation:
Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
L. BRUCE RICMOND
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Abstract

Let [Mscr ]n,k(S) be the set of n-edge k-vertex rooted maps in some class on the surface S. Let P be a planar map in the class. We develop a method for showing that almost all maps in [Mscr ]n,k(S) contain many copies of P. One consequence of this is that almost all maps in [Mscr ]n,k(S) have no symmetries. The classes considered include c-connected maps (c [les ] 3) and certain families of degree restricted maps.

Type
Research Article
Copyright
1997 Cambridge University Press

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