# Multiplicity-Free Gonality on Graphs

@inproceedings{Dean2021MultiplicityFreeGO, title={Multiplicity-Free Gonality on Graphs}, author={Frances Dean and Max Everett and Ralph Morrison}, year={2021} }

The divisorial gonality of a graph is the minimum degree of a positive rank divisor on that graph. We introduce the multiplicity-free gonality of a graph, which restricts our consideration to divisors that place at most 1 chip on each vertex. We give a sufficient condition in terms of vertex-connectivity for these two versions of gonality to be equal; and we show that no function of gonality can bound multiplicity-free gonality, even for simple graphs. We also prove that multiplicity-free… Expand

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