Corrigendum to "SPN graphs: when copositive $=$ SPN"

Abstract

In this corrigendum, an error in the proof of a theorem in [Linear Algebra and its Applications 509 (2016) 82--113] is pointed out. This theorem states that every graph $T_n$ consisting of $n-2$ triangles sharing a common base is SPN. An alternative proof is given here for the case $n=5$, but for all $n>5$ it remains open whether $T_n$ is SPN. As a result, the question whether $K_{2,n}$, $n>4$, is SPN also remains open.