Vol. 9, No. 4, 2016

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Gonality of random graphs

Andrew Deveau, David Jensen, Jenna Kainic and Dan Mitropolsky

Vol. 9 (2016), No. 4, 715–720
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.

Keywords
random graphs, gonality, chip-firing, Brill–Noether theory
Mathematical Subject Classification 2010
Primary: 05C80, 14H51, 14T05
Milestones
Received: 22 July 2015
Revised: 28 August 2015
Accepted: 30 August 2015
Published: 6 July 2016

Communicated by Ravi Vakil
Authors
Andrew Deveau
Yale University
New Haven, CT 06511
United States
David Jensen
Department of Mathematics
University of Kentucky
719 Patterson Office Tower
Lexington, KY 40506
United States
Jenna Kainic
Yale University
New Haven, CT 06511
United States
Dan Mitropolsky
Yale University
New Haven, CT 06511
United States