Many touchings force many crossings

DOI10.1016/j.jctb.2018.12.002zbMath1416.05085OpenAlexW2705173275WikidataQ128760581 ScholiaQ128760581MaRDI QIDQ2312603

János Pach, Géza Tóth

Publication date: 17 July 2019

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: http://real.mtak.hu/102413/1/1706.06829

zbMATH Keywords

crossingplanar curvetouching

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Erd?s problems and related topics of discrete geometry (52C10)

Cites Work

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• How many ways can one draw a graph?
• Improved bounds for planar \(k\)-sets and related problems
• Lower bounds on the number of crossing-free subgraphs of \(K_N\)
• A Separator Theorem for String Graphs and its Applications
• Crossing-Free Subgraphs
• Crossing Numbers and Hard Erdős Problems in Discrete Geometry
• Beyond the Richter-Thomassen Conjecture
• New bounds on curve tangencies and orthogonalities
• The Clarkson–Shor Technique Revisited and Extended
• Toward a theory of crossing numbers
• Distinct distances in the plane

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