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Maximizing the Degree of (Geometric) Thickness-t Regular Graphs

  • Christian A. Duncan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9411)

Abstract

In this paper, we show that there exist \((6t-1)\)-regular graphs with thickness t, by constructing such an example graph. Since all graphs of thickness t must have at least one node with degree less than 6t, this construction is optimal. We also show, by construction, that there exist 5t-regular graphs with geometric thickness at most t. Our construction for the latter builds off of a relationship between geometric thickness and the Cartesian product of two graphs.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceQuinnipiac UniversityHamdenUSA

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