5 problems

Let $P_m$ and $P_n$ be paths on $m$ and $n$ vertices, respectively, and let $\mathfrak{pr}(G)$ denote the minimum coprime number of a graph $G$. Asplund–Fox's path-join conjecture.…

Let $K_n$ be the complete graph on $n$ vertices, let $\overline{K}_m$ be the edgeless graph on $m$ vertices, and let $\mathfrak{pr}(G)$ denote the minimum coprime number of a graph…

Let $K_n$ be the complete graph on $n$ vertices, let $\overline{K}_m$ be the edgeless graph on $m$ vertices, and let $K_n\odot\overline{K}_m$ denote their corona. Let $\pi(x)$ be t…

Let $P_m$ and $P_n$ be paths on $m+1$ and $n+1$ vertices, respectively, and let $P_m+P_n$ denote their graph join. The minimum coprime number $\mathfrak{pr}(G)$ is the least $M$ fo…

Let $K_n$ be the complete graph on $n$ vertices, let $\overline{K}_m$ be the empty graph on $m$ vertices, and let $K_n\odot\overline{K}_m$ denote their corona. Write $\pi(x)$ for t…