On positive hypergraphs

Abstract

Camarena, Csóka, Hubai, Lippner, and Lovász introduced the notion of positive graphs. This notion naturally extends to $r$-uniform hypergraphs. In the case when $r$ is odd, we prove that a hypergraph is positive if and only if its Levi graph is positive. As an application, we show that the $1$-subdivision of $K_{r,r}$ is not a positive graph when $r$ is odd.

arXiv commentfinal version accepted by European Journal of Combinatorics