Graph Treewidth and Geometric Thickness Parameters
نویسندگان
چکیده
منابع مشابه
Graph Treewidth and Geometric Thickness Parameters
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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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 further restricting the vertices to be in convex position, we obtain the book thickness. This paper studies the relat...
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We give asymptotically exact values for the treewidth tw(G) of a random geometric graph G ∈ G(n, r) in [0, √ n]. More precisely, let rc denote the threshold radius for the appearance of the giant component in G(n, r). We then show that for any constant 0 < r < rc, tw(G) = Θ( logn log logn ), and for c being sufficiently large, and r = r(n) ≥ c, tw(G) = Θ(r √ n). Our proofs show that for the cor...
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We give asymptotically exact values for the treewidth tw(G) of a random geometric graph G(n, r) in [0, √ n]. More precisely, we show that there exists some c1 > 0, such that for any constant 0 < r < c1, tw(G) = Θ( logn log logn ), and also, there exists some c2 > c1, such that for any r = r(n) ≥ c2, tw(G) = Θ(r √ n). Our proofs show that for the corresponding values of r the same asymptotic bou...
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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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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2007
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-007-1318-7