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- W4300394423 abstract "It is shown that for a constant $tin mathbb{N}$, every simple topological graph on $n$ vertices has $O(n)$ edges if it 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 $K_{t,t}$-free). As an application, we settle the emph{tangled-thrackle} conjecture formulated by Pach, Radoiv{c}i'c, and T'oth: 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.
- W4300394423 created "2022-10-03" @default.
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- W4300394423 date "2014-06-10" @default.
- W4300394423 modified "2023-09-23" @default.
- W4300394423 title "Disjoint edges in topological graphs and the tangled-thrackle conjecture" @default.
- W4300394423 doi "https://doi.org/10.48550/arxiv.1406.2726" @default.
- W4300394423 hasPublicationYear "2014" @default.
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