A note on the Nearly Dispersability of Odd Toroidal Grids

TL;DR

This paper discusses the nearly dispersability of odd toroidal grids, providing a brief proof for the previously determined matching book thickness related to these graphs.

Contribution

It offers a concise proof confirming the nearly dispersability of odd toroidal grids, building on prior results.

Findings

Odd toroidal grids are nearly dispersable.

Matching book thickness of these grids is elta(G)+1.

Provides a simplified proof of the main result.

Abstract

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 $mbt(G)=\Delta(G)$, \emph{nearly dispersable} if $mbt(G)=\Delta(G)+1$. 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.