Gonality of random graphs

Andrew Deveau; David Jensen; Jenna Kainic; Dan Mitropolsky

doi:10.2140/involve.2016.9.715

Gonality of random graphs

Andrew Deveau, David Jensen, Jenna Kainic, Dan Mitropolsky

Mathematics

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

6 Scopus citations

Abstract

The gonality of a graph is a discrete analogue of the similarly named geometric invariant of algebraic curves. Motivated by recent progress in Brill–Noether theory for graphs, we study the gonality of random graphs. In particular, we show that the gonality of a random graph is asymptotic to the number of vertices.

Original language	English
Pages (from-to)	715-720
Number of pages	6
Journal	Involve
Volume	9
Issue number	4
DOIs	https://doi.org/10.2140/involve.2016.9.715
State	Published - 2016

Bibliographical note

Funding Information:
This paper was written as part of the 2014 Summer Undergraduate Math Research at Yale (SUMRY) program. We would like to extend our thanks to everyone involved in the program, and in particular to Sam Payne, who suggested this project. We also thank Matt Kahle for a particularly fruitful discussion.

Publisher Copyright:
© 2016, Mathematical Sciences Publishers. All rights reserved.

Keywords

Brill–Noether theory
chip-firing
gonality
random graphs

ASJC Scopus subject areas

Mathematics (all)

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10.2140/involve.2016.9.715

Cite this

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AU - Kainic, Jenna

AU - Mitropolsky, Dan

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N2 - The gonality of a graph is a discrete analogue of the similarly named geometric invariant of algebraic curves. Motivated by recent progress in Brill–Noether theory for graphs, we study the gonality of random graphs. In particular, we show that the gonality of a random graph is asymptotic to the number of vertices.

AB - The gonality of a graph is a discrete analogue of the similarly named geometric invariant of algebraic curves. Motivated by recent progress in Brill–Noether theory for graphs, we study the gonality of random graphs. In particular, we show that the gonality of a random graph is asymptotic to the number of vertices.

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Gonality of random graphs

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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