Uniform scrambles on graphs
Combinatorics
2023-08-04 v2 Algebraic Geometry
Abstract
A scramble on a connected multigraph is a collection of connected subgraphs that generalizes the notion of a bramble. The maximum order of a scramble, called the scramble number of a graph, was recently developed as a tool for lower bounding divisorial gonality. We present results on the scramble of all connected subgraphs with a fixed number of vertices, using these to calculate scramble number and gonality both for large families of graphs, and for specific examples like the - and -dimensional hypercube graphs. We also study the computational complexity of the egg-cut number of a scramble.
Keywords
Cite
@article{arxiv.2108.09821,
title = {Uniform scrambles on graphs},
author = {Lisa Cenek and Lizzie Ferguson and Eyobel Gebre and Cassandra Marcussen and Jason Meintjes and Ralph Morrison and Liz Ostermeyer and Shefali Ramakrishna},
journal= {arXiv preprint arXiv:2108.09821},
year = {2023}
}
Comments
13 pages, 9 figures