On the Number of Edges in Geometric Graphs Without Empty Triangles
نویسندگان
چکیده
In this paper we study the extremal type problem arising from the question: What is the maximum number ET (S) of edges that a geometric graph G on a planar point set S can have such that it does not contain empty triangles? We prove: ( n 2 ) −O(n log n) ≤ ET (n) ≤ ( n 2 ) − ( n− 2 + ⌊n 8 ⌋) . keywords: Geometric graphs Empty triangles Combinatorial Geometry Extremal Problem ∗Partially supported by SEP-CONACYT of Mexico. email : [email protected] †Partially supported by SEP-CONACYT of Mexico. email : [email protected] ‡Partially supported by projects MEC MTM2009-07242, Gen. Cat. DGR2009SGR1040, and the ESF EUROCORES programme EuroGIGA, CRP ComPoSe, MICINN Project EUI-EURC-2011-4306. §Partially supported by SEP-CONACYT of Mexico. email : [email protected] ¶Partially supported by projects MTM2009-07242, Gen. Cat. DGR2009GR1040, and the ESF EUROCORES programme EuroGIGA-ComPoSe IP04-MICINN Project EUIEURC-2011-4306. ‖Partially supported by projects MTM2006-03909 (Spain) and SEP-CONACYT of México, Proyecto 80268.
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ورودعنوان ژورنال:
- Graphs and Combinatorics
دوره 29 شماره
صفحات -
تاریخ انتشار 2013