Codes and Expansions (CodEx) Seminar

Afonso Bandeira (ETH Zurich)
The hypergraph Moore bound

The hypergraph Moore bound conjectured by Feige (2008) controls the size of the smallest even cover in a \(k\)-uniform hypergraph in terms of the average density of hyperedges. An even cover is a set of hyperedges covering each vertex an even number of times, generalizing the notion of a cycle in a graph, so the size of the smallest non-trivial even cover provides a notion of hypergraph girth. Recent work, starting from the breakthrough result of Guruswami, Kothari, and Manohar (2022) proved the conjecture up to polylogarithmic factors, whose exponents were later gradually improved. In this talk we will present a simple proof of Feige's original hypergraph Moore bound conjecture for all even \(k\), with no superfluous polylogarithmic factors. If time permits, we will show how the argument can be extended to the case of odd \(k\) by adapting a procedure in [GKM22].

Joint work with Tim Kunisky, Petar Nizic-Nikolac, Lucas Pesenti, and Robert Wang.