Small distances in convex polygons

DOI10.1016/j.disc.2013.05.007zbMath1277.05053OpenAlexW2048564076MaRDI QIDQ385726

Filip Morić

Publication date: 3 December 2013

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

Full work available at URL: https://doi.org/10.1016/j.disc.2013.05.007

zbMATH Keywords

convex polygonsdistance graphssmall distances

Mathematics Subject Classification ID

Distance in graphs (05C12) Convex sets in (3) dimensions (including convex surfaces) (52A15)

Related Items (1)

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

Cites Work

• On the graph of large distances
• On the distribution of distances in finite sets in the plane
• On large distances in planar sets
• A lower bound on the number of unit distances between the vertices of a convex polygon
• The maximum number of second smallest distances in finite planar sets
• The maximum number of unit distances in a convex \(n\)-gon
• The shortest distance among points in general position.
• Research Problems in Discrete Geometry
• How Many Unit Equilateral Triangles Can Be Generated by N Points in Convex Position?
• 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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