Graphs of scramble number two
Combinatorics
2022-12-21 v1 Algebraic Geometry
Abstract
The scramble number of a graph provides a lower bound for gonality and an upper bound for treewidth, making it a graph invariant of interest. In this paper we study graphs of scramble number at most two, and give a classification of all such graphs with a finite list of forbidden topological minors. We then prove that there exists no finite list of forbidden topological minors to characterize graphs of any fixed scramble number greater than two.
Keywords
Cite
@article{arxiv.2212.09949,
title = {Graphs of scramble number two},
author = {Robin Eagleton and Ralph Morrison},
journal= {arXiv preprint arXiv:2212.09949},
year = {2022}
}
Comments
14 pages, 15 figures