Kevin Buchin ; Bettina Speckmann ; Sander Verdonschot - On the number of regular edge labelings

dmtcs:2085 - Discrete Mathematics & Theoretical Computer Science, October 20, 2014, Vol. 16 no. 3 - https://doi.org/10.46298/dmtcs.2085
On the number of regular edge labelingsArticle

Authors: Kevin Buchin ORCID1; Bettina Speckmann ORCID1; Sander Verdonschot 2

  • 1 Department of mathematics and computing science [Eindhoven]
  • 2 School of Computer Science (Carleton, Ottawa)

We prove that any irreducible triangulation on n vertices has O(4.6807n) regular edge labelings and that there are irreducible triangulations on n vertices with Ω(3.0426n) regular edge labelings. Our upper bound relies on a novel application of Shearer's entropy lemma. As an example of the wider applicability of this technique, we also improve the upper bound on the number of 2-orientations of a quadrangulation to O(1.87n).


Volume: Vol. 16 no. 3
Section: Combinatorics
Published on: October 20, 2014
Submitted on: December 27, 2011
Keywords: regular edge labeling,counting,Shearer’s entropy lemma,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Funder: Natural Sciences and Engineering Research Council of Canada
  • A framework for progressive, user-steered algorithms in visual analytics; Funder: Natural Sciences and Engineering Research Council of Canada; Code: 612.001.207
  • Algorithmic Foundations for the Analysis and Visualization of Complex Moving Objects; Funder: Natural Sciences and Engineering Research Council of Canada; Code: 639.023.208

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