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Geometric Thickness of Complete Graphs

Dillencourt, Michael B. and Eppstein, David and Hirschberg, Daniel S. (1998) Geometric Thickness of Complete Graphs. In Whitesides, Sue H., Eds. Proceedings Graph Drawing, pages pp. 102-110, Montréal, Canada.

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Abstract

We define the geometric thickness of a graph to be the smallest number of layers such that we can draw the graph in the plane with straight-line edges and assign each edge to a layer so that no two edges on the same layer cross. The geometric thickness lies between two previously studied quantities, the (graph-theoretical) thickness and the book thickness. We investigate the geometric thickness of the family of complete graphs, {K_n} . We show that the geometric thickness of K_n lies between \lceil (n/5.646)+0.342 \rceil and \lceil n/4 \rceil, and we give exact values of the geometric thickness of K_n for n \le 12 and n \in {15,16}.

Display Formats:BibTex
EPrint Type:Conference Paper
Subjects:M Methods > M.999 Others
M Methods > M.500 Layered
G Algorithms and Complexity > G.700 Layering
P Styles > P.720 Straight-line
Z Theory > Z.250 Geometry
G Algorithms and Complexity > G.999 Others
G Algorithms and Complexity > G.420 Crossings
P Styles > P.480 Layered
ID Code:287
Deposited By:Arnopolina, Galina
Deposited On:09 November 2004
Alternative Locations:http://www.springerlink.com/openurl.asp?genre=article&issn=0302-9743&volume=1547&spage=102

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