Multiplicity-free gonality on graphs
| Main Authors: | Dean, Frances; Department of Mathematics, University of California Berkeley, Berkeley, CA, USA, Everett, Max; Department of Mathematics, City University of New York, New York, NY, USA, Morrison, Ralph; Departments of Mathematics and Statistics, Williams College, Williamstown, MA 01267 |
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| Other Authors: | National Science Foundation, the Williams College SMALL REU |
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2023
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| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/1545 https://www.ejgta.org/index.php/ejgta/article/view/1545/pdf_268 |
Daftar Isi:
- 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 gonality is NP-hard to compute, while still determining it for graph families for which gonality is currently unknown. We also present new gonalities, such as for the wheel graphs.