A New Lower Bound on Graph Gonality
Combinatorics
2021-11-08 v2 Algebraic Geometry
Abstract
We define a new graph invariant called the scramble number. We show that the scramble number of a graph is a lower bound for the gonality and an upper bound for the treewidth. Unlike the treewidth, the scramble number is not minor monotone, but it is subgraph monotone and invariant under refinement. We compute the scramble number and gonality of several families of graphs for which these invariants are strictly greater than the treewidth.
Keywords
Cite
@article{arxiv.2006.01020,
title = {A New Lower Bound on Graph Gonality},
author = {Michael Harp and Elijah Jackson and David Jensen and Noah Speeter},
journal= {arXiv preprint arXiv:2006.01020},
year = {2021}
}
Comments
updated version, minor changes