Abundance: Asymmetric Graph Removal Lemmas and Integer Solutions to Linear Equations

• Main Authors: Girão, António, Hurley, Eoin, Illingworth, Freddie, Michel, Lukas
• Format: Journal Article
• Language: English
• Published: 27.10.2023
• Subjects: Mathematics - Combinatorics; Mathematics - Number Theory

We prove that a large family of pairs of graphs satisfy a polynomial dependence in asymmetric graph removal lemmas. In particular, we give an unexpected answer to a question of Gishboliner, Shapira, and Wigderson by showing that for every $t \geqslant 4$, there are $K_t$-abundant graphs of chromatic...