3 problems

Let $\Sigma$ be a signed graph. Denote by $p^-(\Sigma)$ the maximum number of edge-disjoint negative cycles, by $l(\Sigma)$ its frustration index, and by $p(\Sigma)$ the maximum nu…

Let $K_{n_1,n_2,\ldots,n_k}$ be a complete multipartite graph with $k\geq 3$. Let $-K_{n_1,n_2,\ldots,n_k}$ denote the signature in which every edge is negative, and write $l(-G)$…

Let $(G,\sigma)$ be a signed connected simple subcubic graph, where $v(G)$ denotes the number of vertices of $G$, $F(G,\sigma)$ denotes its frustration index, and the girth is the…