Recursive Generation of 5-Regular Planar Graphs

Hasheminezhad, Mahdieh; McKay, Brendan D.; Reeves, Tristan

doi:10.1007/978-3-642-00202-1_12

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“…Theorem 1 appeared first in [8]. We wish to thank Mohammadreza Jooyandeh, Gordon Royle, and the anonymous referees for useful advice.…”

Section: Discussionmentioning

confidence: 98%

Recursive generation of simple planar 5-regular graphs and pentangulations

Hasheminezhad¹,

McKay²,

Reeves³

2011

JGAA

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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(n 2 ) per isomorphism class. A similar result is obtained for simple planar pentangulations with minimum degree 2.

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“…Theorem 1 appeared first in [8]. We wish to thank Mohammadreza Jooyandeh, Gordon Royle, and the anonymous referees for useful advice.…”

Section: Discussionmentioning

confidence: 98%