We overview the recent resolution of a 1985 open problem of Gyárfás, that chromatic number is polynomially bounded by clique number for graphs with no induced five-vertex path. The proof introduces a chromatic density framework involving chromatic quasirandomness and chromatic density increment, which allows us to deduce the desired statement from the Erdős–Hajnal result for the five-vertex path.
The 2024 summer school was held at IBS for 2 weeks at IBS with lectures by Boris Bukh (CMU) and Tung Nguyen (Princeton University)
The 2024 summer school was held at IBS for two weeks, from July 29 to August 9, 2024. It was organized by the IBS Extremal Combinatorics and Probability Group and featured lectures by Boris Bukh from Carnegie Mellon University and Tung Nguyen from Princeton University.
24.08.09, Tung Nguyen, Recent work on the Erdős-Hajnal conjecture: day 5
24.08.08, Recent work on the Erdős-Hajnal conjecture: day 4
24.08.07, Tung Nguyen, Recent work on the Erdős-Hajnal conjecture: day 3
24.08.06, Tung Nguyen, Recent work on the Erdős-Hajnal conjecture: day 2
24.08.05. Tung Nguyen, Recent work on the Erdős-Hajnal conjecture: day 1
24.08.02, Boris Bukh, Algebraic methods in combinatorics: day 5
24.08.01, Boris Bukh, Algebraic methods in combinatorics: day 4
24.07.31, Boris Bukh, Algebraic methods in combinatorics: day 3
24.07.30, Boris Bukh, Algebraic methods in combinatorics: day 2
24.07.29, Boris Bukh, Algebraic methods in combinatorics: day 1