Disjoint edges in topological graphs
نویسندگان
چکیده
منابع مشابه
Disjoint Edges in Topological Graphs
A topological graph G is a graph drawn in the plane so that its edges are represented by Jordan arcs. G is called simple, if any two edges have at most one point in common. It is shown that the maximum number of edges of a simple topological graph with n vertices and no k pairwise disjoint edges is O (
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A simple topological graph is a graph drawn in the plane so that its edges are represented by continuous arcs with the property that any two of them meet at most once. Using a new tool developed in [12] we show that every simple topological graph on n vertices contains Ω(n 1 2 / √ log n) pairwise disjoint edges. This improves the previous lower bound of Ω(n 1 3 ) by Suk [17] and by Fulek and Ru...
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It is shown that for a constant t ∈ N, every simple topological graph on n vertices has O(n) edges if the graph has no two sets of t edges such that every edge in one set is disjoint from all edges of the other set (i.e., the complement of the intersection graph of the edges is Kt,t-free). As an application, we settle the tangled-thrackle conjecture formulated by Pach, Radoičić, and Tóth: Every...
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A stract. Answering an old question in com inatorial geometry, we show that any configuration consisting of a set V of n points in general position in the plane and a set of 6n-5 closed straight line segments whose endpoints lie in V, contains three pairwise disjoint line segments. A geometric graph is a pair G=(V, E), where V is a set of points (=vertices) in general position in the plane, i ....
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A topological graph drawn on a cylinder whose base is horizontal is angularly monotone if every vertical line intersects every edge at most once. Let c(n) denote the maximum number c such that every simple angularly monotone drawing of a complete graph on n vertices contains at least c pairwise disjoint edges. We show that for every simple complete topological graph G there exists ∆, 0 < ∆ < n,...
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2010
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2010.v1.n3.a4