Journal of Graph Algorithms and Applications
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Special Issue on Selected Papers from the Third Annual Workshop on Algorithms and Computation (WALCOM 2009)
Recursive generation of simple planar 5-regular graphs and pentangulations
Vol. 15, no. 3, pp. 417-436, 2011. Regular paper.
Abstract We describe how the 5-regular simple planar graphs can all be obtained from an elementary family of starting graphs by repeatedly applying a few local expansion operations. The proof uses an amalgam of theory and computation. By incorporating the recursion into the canonical construction path method of isomorph rejection, a generator of non-isomorphic embedded 5-regular planar graphs is obtained with time complexity O(n2) per isomorphism class. A similar result is obtained for simple planar pentangulations with minimum degree 2.
Submitted: May 2009.
Reviewed: January 2010.
Revised: April 2010.
Accepted: October 2010.
Final: November 2010.
Published: July 2011.