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 subdivision. We compute the scramble number and gonality of several families of graphs for which these invariants are strictly greater than the treewidth.
| Original language | English |
|---|---|
| Pages (from-to) | 172-179 |
| Number of pages | 8 |
| Journal | Discrete Applied Mathematics |
| Volume | 309 |
| DOIs | |
| State | Published - Mar 15 2022 |
Bibliographical note
Publisher Copyright:© 2021 Elsevier B.V.
Funding
This research was conducted as a project with the University of Kentucky Math Lab. The third author was supported by NSF DMS-1601896 . We would like to thank Ralph Morrison for some discussions on this material. We would also like to thank the anonymous referees for several helpful comments, including the suggestion to add Examples 4.8 and 4.9 . This research was conducted as a project with the University of Kentucky Math Lab. The third author was supported by NSF DMS-1601896. We would like to thank Ralph Morrison for some discussions on this material. We would also like to thank the anonymous referees for several helpful comments, including the suggestion to add Examples 4.8 and 4.9.
| Funders | Funder number |
|---|---|
| University of Kentucky Math Lab | |
| National Science Foundation Arctic Social Science Program | DMS-1601896 |
Keywords
- Chip-firing
- Gonality
- Treewidth
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics