## Abstract

Stable gonality is a multigraph parameter that measures the complexity of a graph. It is defined using maps to trees. Those maps, in some sense, divide the edges equally over the edges of the tree; stable gonality asks for the map with

the minimum number of edges mapped to each edge of the tree. This parameter is related to treewidth, but unlike treewidth, it distinguishes multigraphs from their underlying simple graphs. Stable gonality is relevant for problems in number theory. In this paper, we show that deciding whether the stable gonality of a given graph is at most a given integer k belongs to the class NP, and we give an algorithm that computes the stable gonality of a graph in O((1.33n) nmmpoly(n, m)) time.

the minimum number of edges mapped to each edge of the tree. This parameter is related to treewidth, but unlike treewidth, it distinguishes multigraphs from their underlying simple graphs. Stable gonality is relevant for problems in number theory. In this paper, we show that deciding whether the stable gonality of a given graph is at most a given integer k belongs to the class NP, and we give an algorithm that computes the stable gonality of a graph in O((1.33n) nmmpoly(n, m)) time.

Original language | English |
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Number of pages | 14 |

Journal | Discrete Mathematics and Theoretical Computer Science |

Volume | 21 |

Issue number | 1 |

Publication status | Published - Jun 2019 |

## Keywords

- Algorithm
- gonality
- graph parameter