Recognizing circle graphs in polynomial time
Journal of the ACM (JACM)
Reducing prime graphs and recognizing circle graphs
Combinatorica
Detecting and decomposing self-overlapping curves
Computational Geometry: Theory and Applications
Journal of Algorithms
A constructive enumeration of fullerenes
Journal of Algorithms
Graph classes: a survey
Boundary uniqueness of fuseness
Discrete Applied Mathematics
A constructive enumeration of nanotube caps
Discrete Applied Mathematics
Filling of a given boundary by p-gons and related problems
Discrete Applied Mathematics
Efficiently implementing maximum independent set algorithms on circle graphs
Journal of Experimental Algorithmics (JEA)
Self-overlapping curves revisited
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Finding Fullerene Patches in Polynomial Time
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
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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.