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22nd Cumberland Conference on Combinatorics, Graph Theory and Computing
May 21-23, 2009
Western Kentucky University
Bowling Green, KY, USA

Organizers
Bela Csaba, Chair; Mustafa Atici; Robert Crawford; Claus Ernst; Dominic Lanphier; Attila Por

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Counting and Generating 4-Regular Hamiltonian Plane Graphs
by
Uta Ziegler
Western Kentucky University
Coauthors: O. Ascigil, Y. Diao, C. Ernst, D. High

This talk describes a special class of graphs which are of interest in knot theory. The graphs are 4-regular plane graphs which are Hamiltonian. The exact count of the number of such graphs for a given n is discussed and their asymptotic growth rate. We present an algorithm to generate such graphs in O(n) time and present numerical evidence which suggests that the algorithm can be modified to generate these graphs with near random probability.

Date received: April 30, 2009

Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cayq-57.