A note on the Nearly Dispersability of Odd Toroidal Grids

The \emph{matching book thickness} $mbt(G)$ of $G$ is the minimum integer $m$ such that an $m$-page matching book embedding exists. A graph $G$ is called \emph{dispersable} if $mbt(G)=\mathrm{\Delta }(G)$, \emph{nearly dispersable} if $mbt(G)=\mathrm{\Delta }(G)+1$. Recently, the authors determined the nearly dispersability of odd toroidal grids $T_{s,t}$. In this note, we further present a brief proof for this result.