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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 straightline 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, {Kn}. We show that the geometric thickness of Kn lies... (Update)
Context of citations to this paper: More
.... thickness, defined to be the minimum number of layers for which a drawing of G exists having all edges drawn as straight line segments [11]. Finally, the book thickness of a graph G is the minimum number of layers for which a drawing of G exists, in which edges are drawn as...
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6: The book thickness of a graph (context) - Bernhart, Kainen - 1979
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BibTeX entry: (Update)
Michael B. Dillencourt, David Eppstein, and Daniel S. Hirschberg. Geometric Thickness of Complete Graphs. Journal of Graph Algorithms and Applications, 4:5--17, 2000. http://citeseer.ist.psu.edu/dillencourt00geometric.html More
@article{ dillencourt98geometric,
author = "Michael B. Dillencourt and David Eppstein and Daniel S. Hirschberg",
title = "Geometric Thickness of Complete Graphs",
journal = "Lecture Notes in Computer Science",
volume = "1547",
pages = "102--110",
year = "1998",
url = "citeseer.ist.psu.edu/dillencourt00geometric.html" }
Citations (may not include all citations):36 The book thickness of a graph (context) - Bernhart, Kainen - 1979
16 Bounds for rectilinear crossing numbers (context) - Bienstock, Dean - 1993
16 On representation of some thickness-two graphs (context) - Hutchinson, Shermer et al. - 1995
15 Some provably hard crossing number problems (context) - Bienstock - 1991
14 Pearls in Graph Theory (context) - Hartsfield, Ringel - 1990
12 Determining the thickness of a graph is NP-hard (context) - Mansfield - 1983
12 the thickness of graphs of given degree (context) - Halton - 1991
11 The decomposition of complete graphs into planar subgraphs (context) - Beineke - 1967
8 On heuristics for determining the thickness of a graph - Cimikowski - 1995
8 The thickness of the complete graph (context) - Beineke, Harary - 1965
4 en trois graphes planaires (context) - Mayer - 1972
3 Which crossing number is it (context) - Pach, Toth - 1998
3 Abhandlungen aus dem Mathematischen Seminar der Universitat .. (context) - Kainen, coarseness - 1973
2 The thickness of the complete graph having 6m +4points (context) - Vasak
1 The thickness of an arbitrary complete graph (context) - AlekseevandV, Goncakov - 1976
1 Mathematics with Applications (context) - Beineke, survey - 1997
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