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

Duncan, Christian A. (2015) Maximizing the Degree of (Geometric) Thickness-t Regular Graphs. In: Graph Drawing and Network Visualization: 23rd International Symposium, GD 2015, September 24-26, 2015 , pp. 199-204(Official URL:

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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.

Item Type: Conference Paper
Classifications: G Algorithms and Complexity > G.999 Others
P Styles > P.540 Planar
P Styles > P.720 Straight-line
Z Theory > Z.999 Others

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