Tesar Abstract

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Tesar Abstract

Some Extensions of the Genus Distribution of Closed-End Ladders

Esther Tesar, Department of Mathematics, Drew University

The genus distribution for a class of graphs called closed-end ladders was found by Furst, Gross and Statman. Their techniques can be extended to find probability polynomials (a generalization of the genus distribution of a cubic graph that instead of requiring each imbedding to be equally likely depends on a arbitrary probability p) for closed-end ladders. A second extension that we make is using the genus distribution of closed-end ladders to find the genus distribution of Ringel ladders. We then use this to find the average genus and to look at the probability of finding an imbedding with one region used by Ringel and Youngs in their proof of the Heawood Map Coloring Theorem.