Dr Anil Kumar C P, Associate Professor, Mathematics, SIAS gave a talk at the Chennai Combinatorics Day conference on Wednesday, July 29, 2026 at Chennai Mathematical Institute. The talk was titled ‘Recent developments on the bichromatic triangle conjecture’.
Abstract
In this talk, Dr Kumar discussed recent developments on the bichromatic triangle conjecture, after some preliminaries and old results.
In particular he introduced block bicolored arrangements and prove that the bichromatic triangle conjecture holds for them. The speaker also showed that any bicoloring with at most five of one color has a bichromatic triangle. Then they prove the latest result, proved in January 2026 by Y. A. Radtke, B. Keszegh and R. Lauff, that in every simple Euclidean pseudoline arrangement colored by two colors red and blue, either there exists a bichromatic triangle or a red-red-blue-blue quadrangle. There was also mention of some more recent results by the same three authors on the maximum sizes of independence numbers of the (pseudo)line-face hypergraphs and (pseudo)line-triangle hypergraphs.
