冰袋突变等价的复杂性

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Annals of Combinatorics Pub Date : 2023-11-04 DOI:10.1007/s00026-023-00668-w

David Soukup

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引用次数: 0

摘要

我们证明了确定冰袋是否突变等价于具有给定性质的冰袋的np -硬度结果，特别是确定冰袋是否突变等价于任意两个顶点之间有恰好k个箭头的冰袋是np -硬度结果。此外，确定一个冰袋是否与一个冻结顶点之间没有边缘的冰袋突变等效是强np困难的。最后，我们给出了具有两个可变顶点的冰颤的突变类的一个表征。

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Complexity of Ice Quiver Mutation Equivalence

We prove NP-hardness results for determining whether ice quivers are mutation equivalent to quivers with given properties, specifically, determining whether an ice quiver is mutation equivalent to an ice quiver with exactly k arrows between any two of its vertices is NP-hard. Also, determining whether an ice quiver is mutation equivalent to a quiver with no edges between frozen vertices is strongly NP-hard. Finally, we present a characterization of mutation classes of ice quivers with two mutable vertices.

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来源期刊

Annals of Combinatorics 数学-应用数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annals of Combinatorics publishes outstanding contributions to combinatorics with a particular focus on algebraic and analytic combinatorics, as well as the areas of graph and matroid theory. Special regard will be given to new developments and topics of current interest to the community represented by our editorial board. The scope of Annals of Combinatorics is covered by the following three tracks: Algebraic Combinatorics: Enumerative combinatorics, symmetric functions, Schubert calculus / Combinatorial Hopf algebras, cluster algebras, Lie algebras, root systems, Coxeter groups / Discrete geometry, tropical geometry / Discrete dynamical systems / Posets and lattices Analytic and Algorithmic Combinatorics: Asymptotic analysis of counting sequences / Bijective combinatorics / Univariate and multivariable singularity analysis / Combinatorics and differential equations / Resolution of hard combinatorial problems by making essential use of computers / Advanced methods for evaluating counting sequences or combinatorial constants / Complexity and decidability aspects of combinatorial sequences / Combinatorial aspects of the analysis of algorithms Graphs and Matroids: Structural graph theory, graph minors, graph sparsity, decompositions and colorings / Planar graphs and topological graph theory, geometric representations of graphs / Directed graphs, posets / Metric graph theory / Spectral and algebraic graph theory / Random graphs, extremal graph theory / Matroids, oriented matroids, matroid minors / Algorithmic approaches