Many Touchings Force Many Crossings

DOI10.1007/978-3-319-73915-1_13zbMath1503.52027arXiv1706.06829OpenAlexW2954071614MaRDI QIDQ4625108

János Pach, Géza Tóth

Publication date: 20 February 2019

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.06829

zbMATH Keywords

crossingplanar curvestouching

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) 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
• Crossings between Curves with Many Tangencies
• Crossing-Free Subgraphs
• 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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