$L_p$ regular sparse hypergraphs
Volume 240 / 2018
Fundamenta Mathematicae 240 (2018), 265-299 MSC: Primary 05C35, 05C65; Secondary 46B25, 60G42. DOI: 10.4064/fm364-2-2017 Published online: 24 July 2017
We study sparse hypergraphs which satisfy a mild pseudorandomness condition known as $L_p$ regularity. We prove appropriate regularity and counting lemmas, and we extend the relative removal lemma of Tao to this setting. This answers a question from a 2014 paper by Borgs, Chayes, Cohn and Zhao.