Multiplicity-Free Gonality on Graphs by Max Everett '21, Mathematics Senior Thesis Defense

Multiplicity-Free Gonality on Graphs by Max Everett ’21, Mathematics Senior Thesis Defense, Monday, April 26, 1:45 – 2:30 pm, live talk can be accessed at https://williams.zoom.us/j/97617951870.

Abstract:  In this thesis we study a new graph invariant which we call multiplicity-free gonality, a relative of divisorial gonality where we are restricted to consideration of divisors that map the vertices of a graph G to {0,1}.  We present a condition to guarantee equality between multiplicity-free gonality and divisorial gonality, as well as a proof demonstrating that divisorial gonality cannot bound multiplicity-free gonality for simple graphs.  We use Dhar’s Burning Algorithm to prove both of these results.  We also present families of graphs with previously-known gonality and multiplicity-free gonality to demonstrate the similarities and differences between these invariants, but we present a novel proof using scramble number, a new graph invariant that acts as a lower bound to gonality.