Counting Hexagonal Patches and Independent Sets in Circle Graphs
Discrete Mathematics
2009-07-15 v2 Data Structures and Algorithms
Abstract
A hexagonal patch is a plane graph in which inner faces have length 6, inner vertices have degree 3, and boundary vertices have degree 2 or 3. We consider the following counting problem: given a sequence of twos and threes, how many hexagonal patches exist with this degree sequence along the outer face? This problem is motivated by the study of benzenoid hydrocarbons and fullerenes in computational chemistry. We give the first polynomial time algorithm for this problem. We show that it can be reduced to counting maximum independent sets in circle graphs, and give a simple and fast algorithm for this problem.
Cite
@article{arxiv.0808.3881,
title = {Counting Hexagonal Patches and Independent Sets in Circle Graphs},
author = {Paul Bonsma and Felix Breuer},
journal= {arXiv preprint arXiv:0808.3881},
year = {2009}
}