Name
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 enumeration 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. It is also shown how to subsequently generate hexagonal patches. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/s00453-011-9561-y | Algorithmica |
Keywords | Field | DocType |
Counting problem,Planar graph,Circle graph,Fullerene,Hexagonal patch,Fusene,Polyhex | Discrete mathematics,Combinatorics,Circle graph,Vertex (geometry),Enumeration,Counting problem,Independent set,Degree (graph theory),Time complexity,Planar graph,Mathematics | Journal |
Volume | Issue | ISSN |
63 | 3 | 0178-4617 |
ISBN | Citations | PageRank |
3-642-12199-3 | 1 | 0.39 |
References | Authors | |
22 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Paul Bonsma | 1 | 287 | 20.46 |
| Felix Breuer | 2 | 22 | 5.35 |