On the dispersability of graph bundles over cycles

TL;DR

This paper investigates the dispersability of Cartesian graph bundles over two cycles, providing a complete characterization based on bipartiteness, and introduces the concept of near dispersability.

Contribution

It offers a complete solution to the dispersability problem for graph bundles over two cycles, highlighting the role of bipartiteness in dispersability.

Findings

Graph bundle over two cycles is dispersable if bipartite.

Graph bundle over two cycles is nearly dispersable if not bipartite.

Complete characterization of dispersability for these graph bundles.

Abstract

In this paper, the dispersability of the Cartesian graph bundle over two cycles is completely solved. We show the Cartesian graph bundle $G$ over two cycles is dispersable if $G$ is bipartite; otherwise, $G$ is nearly dispersable.