TY - JOUR

T1 - Eppstein's bound on intersecting triangles revisited

AU - Nivasch, Gabriel

AU - Sharir, Micha

N1 - Funding Information:
E-mail addresses: [email protected] (G. Nivasch), [email protected] (M. Sharir). 1 Work was supported by ISF Grant 155/05 and by the Hermann Minkowski—MINERVA Center for Geometry at Tel Aviv University. 2 Work was partially supported by NSF grant CCF-05-14079, by a grant from the US–Israel Binational Science Foundation, by ISF Grant 155/05, and by the Hermann Minkowski—MINERVA Center for Geometry at Tel Aviv University.

PY - 2009/2

Y1 - 2009/2

N2 - Let S be a set of n points in the plane, and let T be a set of m triangles with vertices in S. Then there exists a point in the plane contained in Ω (m3 / (n6 log2 n)) triangles of T. Eppstein [D. Eppstein, Improved bounds for intersecting triangles and halving planes, J. Combin. Theory Ser. A 62 (1993) 176-182] gave a proof of this claim, but there is a problem with his proof. Here we provide a correct proof by slightly modifying Eppstein's argument.

AB - Let S be a set of n points in the plane, and let T be a set of m triangles with vertices in S. Then there exists a point in the plane contained in Ω (m3 / (n6 log2 n)) triangles of T. Eppstein [D. Eppstein, Improved bounds for intersecting triangles and halving planes, J. Combin. Theory Ser. A 62 (1993) 176-182] gave a proof of this claim, but there is a problem with his proof. Here we provide a correct proof by slightly modifying Eppstein's argument.

KW - Selection Lemma

KW - Simplex

KW - Triangle

KW - k-set

UR - http://www.scopus.com/inward/record.url?scp=56549107694&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2008.07.003

DO - 10.1016/j.jcta.2008.07.003

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AN - SCOPUS:56549107694

SN - 0097-3165

VL - 116

SP - 494

EP - 497

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 2

ER -