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- W2554500686 abstract "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 n-vertex graph drawn in the plane such that every pair of edges have precisely one point in common, where this point is either a common endpoint, a crossing, or a point of tangency, has at most O(n) edges." @default.
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- W2554500686 date "2016-01-01" @default.
- W2554500686 modified "2023-10-18" @default.
- W2554500686 title "Disjoint edges in topological graphs and the tangled-thrackle conjecture" @default.
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- W2554500686 doi "https://doi.org/10.1016/j.ejc.2015.07.004" @default.
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