2015/03/21 by Michael S. Payne, Payne, Michael S.
Business, Management and Accounting · Engineering · Mathematics · #05D99 (Primary) 51A45 (Secondary) #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Optics and Image Analysis
paper · pdf · doi:10.48550/arxiv.1503.06281
openalex publication_date 2015/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a set of red and blue points in the plane, a bichromatic line is a line containing at least one red and one blue point. We prove the following conjecture of Kleitman and Pinchasi (unpublished, 2003). Let P be a set of n red, and n or n-1 blue points in the plane. If neither colour class is collinear, then P determines at least |P|-1 bichromatic lines. In fact we are able to achieve the same conclusion under the weaker assumption that P is not collinear or a near-pencil.