Empty red-red-blue triangles
Ting-Wei Chao, Zichao Dong, Zhuo Wu

TL;DR
The paper proves a lower bound on the number of empty red-red-blue triangles formed by any balanced bipartition of a general position point set in the plane.
Contribution
It establishes a new combinatorial lower bound of a3(n^{3/2}) for the number of such triangles, advancing understanding of geometric configurations.
Findings
Every balanced bipartition yields a3(n^{3/2}) empty triangles.
The result applies to point sets in general position.
Provides a significant lower bound in geometric combinatorics.
Abstract
Let be a -point set in the plane that is in general position. We prove that every red-blue bipartition of into and with generates red-red-blue empty triangles.
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Taxonomy
TopicsAdvanced Materials and Mechanics · Mathematics and Applications · Structural Analysis and Optimization
