On graph thickness, geometric thickness, and separator theorems
نویسندگان
چکیده
منابع مشابه
On Graph Thickness, Geometric Thickness, and Separator Theorems
We investigate the relationship between geometric thickness and the thickness, outerthickness, and arboricity of graphs. In particular, we prove that all graphs with arboricity two or outerthickness two have geometric thickness O(log n). The technique used can be extended to other classes of graphs so long as a standard separator theorem exists. For example, we can apply it to show the known bo...
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| We nd a large number of \geometric separator theorems" such as: I: Given N disjoint iso-oriented squares in the plane, there exists a rectangle with 2N=3 squares inside, 2N=3 squares outside, and (4 + o(1)) p N partly in & out. II: There exists a rectangle that is crossed by the minimal spanning tree of N sites in the plane at (4 3 1=4 + o(1)) p N points, having 2N=3 sites inside and outside....
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Consider a drawing of a graph G in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of G, is the classical graph parameter thickness. By restricting the edges to be straight, we obtain the geometric thickness. By additionally restricting the vertices to be in convex position, we obtain the book thickness. This paper studies the ...
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We show that graph-theoretic thickness and geometric thickness are not asymptotically equivalent: for every t, there exists a graph with thickness three and geometric thickness ≥ t.
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We show that geometric thickness and book thickness are not asymptotically equivalent: for every t, there exists a graph with geometric thickness two and book thickness ≥ t.
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2011
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2010.09.005