6 problems

Let $G$ be a finite simple graph of order $2n$ with a perfect matching. Write $e(G)$ for the number of edges of $G$, and let $F(G)$ denote its maximum forcing number. Liu–Zhang's c…

Let $G$ be a graph with maximum degree at most $3$, let $n$ be the number of vertices of $G$, and let $F(G)$ denote its forcing number. A $k$-parallel path graph is a graph of $k$-…

Let $G$ be a graph with $n$ vertices and maximum degree $\Delta(G)=3$, and let $F(G)$ denote its forcing number. Gentner–Rautenbach's conjecture. They conjectured that … This conje…

Connected forcing number lower bound conjecture.

Let $G$ be an elementary polyomino, meaning a polyomino whose associated plane bipartite graph is elementary. The maximum forcing number conjecture. The maximum forcing number of…

Let $G=(V,E)$ be a connected graph with maximum degree $\Delta \ge 2$, and let $n$ denote its order. Write $Z(G)$ for the zero-forcing number and $F_1(G)$ for the $1$-forcing numbe…