@article{Aidun2020TreewidthAG,
title={Treewidth and gonality of glued grid graphs},
author={Ivan Aidun and Frances Dean and Ralph Morrison and Teresa Yu and Julie Yuan},
journal={Discret. Appl. Math.},
year={2020},
volume={279},
pages={1-11}
}

A min-max theorem asserting that sbn(G) is equal to the minimum k for which G is a minor of the lexicographic product of a tree and a clique on k vertices is proved and it is proved that every edge-maximal graph of strict bramble number at most k is a k-domino-tree.Expand

The upper bound to prove that Baker's gonality conjecture holds for the Cartesian product of any two graphs with two or more vertices each is presented, and precisely which nontrivial product graphs have gonality equal to Baker's conjectural upper bound is determined.Expand

We prove that the (divisorial) gonality of a finite connected graph is lower bounded by its treewidth. We show that equality holds for grid graphs and complete multipartite graphs.
We prove that the… Expand

The gonality gon(G) of a graph G is the smallest degree of a divisor of positive rank in the sense of Baker-Norine. In this note we show that computing gon(G) is NP-hard by a reduction from the… Expand

It is shown that there are connected graphs of treewidth 2 of arbitrarily high gonality and that there exist pairs of connected graphs such that H has strictly lower gonality than G.Expand

The tree-width of a graph G is the minimum k such that G may be decomposed into a "tree-structure" of pieces each with at most k + l vertices. We prove that this equals the maximum k such that there… Expand

S-functions are mappings from the class of finite graphs into the set of integers, such that certain formal conditions are fulfilled which are shared by the chromatic number, the vertex-connectivity,… Expand