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Stable gonality is computable

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Název: Stable gonality is computable
Autoři: Ragnar Groot Koerkamp, Marieke van der Wegen
Zdroj: Discrete Mathematics & Theoretical Computer Science, Vol vol. 21 no. 1, ICGT 2018 (2019)
Informace o vydavateli: Discrete Mathematics & Theoretical Computer Science, 2019.
Rok vydání: 2019
Sbírka: LCC:Mathematics
Témata: computer science - discrete mathematics, computer science - data structures and algorithms, mathematics - combinatorics, mathematics - number theory, Mathematics, QA1-939
Popis: 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 $O((1.33n)^nm^m \text{poly}(n,m))$ time.
Druh dokumentu: article
Popis souboru: electronic resource
Jazyk: English
ISSN: 1365-8050
Relation: https://dmtcs.episciences.org/4931/pdf; https://doaj.org/toc/1365-8050
DOI: 10.23638/DMTCS-21-1-10
Přístupová URL adresa: https://doaj.org/article/db83f61672e6437c94e66bae01a6c07f
Přístupové číslo: edsdoj.b83f61672e6437c94e66bae01a6c07f
Databáze: Directory of Open Access Journals
Popis
Abstrakt: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 $O((1.33n)^nm^m \text{poly}(n,m))$ time.
ISSN:13658050
DOI:10.23638/DMTCS-21-1-10