4 problems

Let $M(\Delta \leqslant k)$ denote the maximum inversion diameter among graphs whose maximum degree is at most $k$. The complete graph gives $M(\Delta \leqslant k) \geqslant k$. Ma…

Let $K_n$ be the complete graph on $n$ vertices, and let $\mathcal{U}(K_n)$ be its unlabelled inversion graph, obtained by identifying vertices of the inversion graph corresponding…

Let $G$ be a graph, let $t$ be a positive integer, let $\overline{K}_t$ be the edgeless graph on $t$ vertices, and let $G[\overline{K}_t]$ denote the blow-up of $G$ in which each v…

Let $G$ be a graph, let $\mathcal{I}(G)$ be its inversion graph, and let $\Delta(G)$ denote its maximum degree. Inversion diameter conjecture. For every graph $G$, … This would giv…