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arXiv · 2206.06907

Bounds on higher graph gonality

Lisa Cenek·Lizzie Ferguson·Eyobel Gebre·Cassandra Marcussen·Jason Meintjes·Ralph Morrison·Liz Ostermeyer·Shefali Ramakrishna
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Abstract

We prove new lower and upper bounds on the higher gonalities of finite graphs. These bounds are generalizations of known upper and lower bounds for first gonality to higher gonalities, including upper bounds on gonality involving independence number, and lower bounds on gonality by scramble number. We apply our bounds to study the computational complexity of computing higher gonalities, proving that it is NP-hard to compute the second gonality of a graph when restricting to multiplicity-free divisors.

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Lisa Cenek, Lizzie Ferguson, Eyobel Gebre, Cassandra Marcussen, Jason Meintjes, Ralph Morrison, Liz Ostermeyer, Shefali Ramakrishna. 2022-06-14. Bounds on higher graph gonality. https://arxiv.org/abs/2206.06907

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