On the number of occurrences of the \(k\)th smallest distance between points in convex position

DOI10.1016/j.disc.2015.01.019zbMath1371.05066OpenAlexW2095403584MaRDI QIDQ2407030

István Tomon

Publication date: 28 September 2017

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2015.01.019

zbMATH Keywords

convex polygonsdistance graphssmall distances

Mathematics Subject Classification ID

Distance in graphs (05C12) Lattices and convex bodies in (2) dimensions (aspects of discrete geometry) (52C05)

Cites Work

• Small distances in convex polygons
• The maximum number of unit distances in a convex \(n\)-gon
• Research Problems in Discrete Geometry
• On A Problem of P. Erdos
• The maximum number of times the same distance can occur among the vertices of a convex \(n\)-gon is \(O(n\log n)\)

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