A new lower bound on graph gonality

Michael Harp; Elijah Jackson; David Jensen; Noah Speeter

doi:10.1016/j.dam.2021.11.003

A new lower bound on graph gonality

Michael Harp, Elijah Jackson, David Jensen, Noah Speeter

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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	https://doi.org/10.1016/j.dam.2021.11.003
State	Published - Mar 15 2022

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

Chip-firing
Gonality
Treewidth

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2021.11.003

Cite this

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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.",

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AU - Jensen, David

AU - Speeter, Noah

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N2 - 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.

AB - 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.

KW - Chip-firing

KW - Gonality

KW - Treewidth

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UR - http://www.scopus.com/inward/citedby.url?scp=85120946138&partnerID=8YFLogxK

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VL - 309

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EP - 179

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

A new lower bound on graph gonality

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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