A Better Bound for the Pair-Crossing Number

Géza Tóth ()
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Géza Tóth: Hungarian Academy of Sciences, Rényi Institute

A chapter in Thirty Essays on Geometric Graph Theory, 2013, pp 563-567 from Springer

Abstract: Abstract The crossing number cr(G) of a graph G is the minimum possible number of edge crossings in a drawing of G, and the pair-crossing number pair-cr(G) is the minimum possible number of crossing pairs of edges in a drawing of G. Clearly, pair-cr(G) ≤ cr(G). We show that for any graph G, $$\mathrm{cr}(G) = O(\text{ pair-cr}{(G){}^{7/4}\log }^{3/2}(\text{ pair-cr}(G)))$$ .

Keywords: Pair-crossing Number; Edge Crossings; String Graphs; Intersection Graph; Jordan Region (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-0110-0_30

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DOI: 10.1007/978-1-4614-0110-0_30

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