Finding Fullerene Patches in Polynomial Time

  • Paul Bonsma
  • Felix Breuer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)


We consider the following question, motivated by the enumeration of fullerenes. A fullerene patch is a 2-connected plane graph G in which inner faces have length 5 or 6, non-boundary vertices have degree 3, and boundary vertices have degree 2 or 3. The degree sequence along the boundary is called the boundary code of G. We show that the question whether a given sequence S is a boundary code of some fullerene patch can be answered in polynomial time when such patches have at most five 5-faces. We conjecture that our algorithm gives the correct answer for any number of 5-faces, and sketch how to extend the algorithm to the problem of counting the number of different patches with a given boundary code.


Polynomial Time Plane Graph Boundary Edge Sequence Operation Outer Face 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Paul Bonsma
    • 1
  • Felix Breuer
    • 2
  1. 1.Computer Science DepartmentHumboldt Universität zu BerlinBerlin
  2. 2.Mathematics DepartmentFreie Universität BerlinBerlin

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