Eigenvalues of non-regular linear quasirandom hypergraphs.

Chung, Graham, and Wilson proved that a graph is quasirandom if and only if there is a large gap between its first and second largest eigenvalue. Recently, the authors extended this characterization to coregular k -uniform hypergraphs with loops. However, for k ≥ 3 no k -uniform hypergraph is coregular. In this paper we remove the coregular requirement. Consequently, the characterization can be applied to k -uniform hypergraphs; for example it is used in Lenz and Mubayi (2015) [5] to show that a construction of a k -uniform hypergraph sequence has some quasirandom properties. The specific statement that we prove here is that if a k -uniform hypergraph satisfies the correct count of a specially defined four-cycle, then its second largest eigenvalue is much smaller than its largest one. [ABSTRACT FROM AUTHOR]