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arXiv · 2108.09821

Uniform scrambles on graphs

Lisa Cenek·Lizzie Ferguson·Eyobel Gebre·Cassandra Marcussen·Jason Meintjes·Ralph Morrison·Liz Ostermeyer·Shefali Ramakrishna
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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 $4$- and $5$-dimensional hypercube graphs. We also study the computational complexity of the egg-cut number of a scramble.

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Lisa Cenek, Lizzie Ferguson, Eyobel Gebre, Cassandra Marcussen, Jason Meintjes, Ralph Morrison, Liz Ostermeyer, Shefali Ramakrishna. 2021-08-22. Uniform scrambles on graphs. https://arxiv.org/abs/2108.09821

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