Treewidth and gonality of glued grid graphs

TL;DR

This paper calculates the treewidth and divisorial gonality of glued grid graphs, including stacked prism and toroidal grids, using bramble constructions and exploring connections to tropical geometry.

Contribution

It introduces methods to determine treewidth and gonality of glued grid graphs, linking graph theory with tropical geometry.

Findings

Treewidth of glued grid graphs determined using strict brambles.

Divisorial gonality of these graphs computed.

Connections established between graph invariants and tropical geometry.

Abstract

We compute the treewidth of a family of graphs we refer to as the glued grids, consisting of the stacked prism graphs and the toroidal grids. Our main technique is constructing strict brambles of large orders. We discuss connections to divisorial graph theory coming from tropical geometry, and use our results to compute the divisorial gonality of these graphs.