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math.CO2024
Equivalence between Erdős-Hajnal and polynomial Rödl and Nikiforov conjectures
Matija Bucić, Jacob Fox, Huy Tuan Pham
It is well-known that polynomial versions of theorems of Rödl and Nikiforov, as conjectured by Fox and Sudakov and Nguyen, Scott and Seymour imply the classical Erdős-Hajnal conjec…
math.CO2024
A question of Erdős and Graham on Egyptian fractions
David Conlon, Jacob Fox, Xiaoyu He +4
Answering a question of Erdős and Graham, we show that for each fixed positive rational number the number of ways to write as a sum of reciprocals of distinct positive inte…
math.CO2024
A multipartite analogue of Dilworth's Theorem
Jacob Fox, Huy Tuan Pham
We prove that every partially ordered set on elements contains subsets such that either each of these subsets has size and, for every…