Topology of Cut Complexes of Graphs

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-05-24 DOI:10.1137/23m1569034

Margaret Bayer, Mark Denker, Marija Jelić Milutinović, Rowan Rowlands, Sheila Sundaram, Lei Xue

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1630-1675, June 2024.
Abstract. We define the [math]-cut complex of a graph [math] with vertex set [math] to be the simplicial complex whose facets are the complements of sets of size [math] in [math] inducing disconnected subgraphs of [math]. This generalizes the Alexander dual of a graph complex studied by Fröberg [Topics in Algebra, Part 2, PWN, Warsaw, 1990, pp. 57–70] and Eagon and Reiner [J. Pure Appl. Algebra, 130 (1998), pp. 265–275]. We describe the effect of various graph operations on the cut complex and study its shellability, homotopy type, and homology for various families of graphs, including trees, cycles, complete multipartite graphs, and the prism [math], using techniques from algebraic topology, discrete Morse theory, and equivariant poset topology.

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图形切割复合物拓扑学

SIAM 离散数学杂志》，第 38 卷第 2 期，第 1630-1675 页，2024 年 6 月。摘要。我们定义顶点集为[math]的图[math]的[math]-切复数为简单复数，其面是[math]中大小为[math]的集合的补集，诱导出[math]的断开子图。这概括了 Fröberg [Topics in Algebra, Part 2, PWN, Warsaw, 1990, pp.我们利用代数拓扑学、离散莫尔斯理论和等变实在拓扑学中的技术，描述了各种图操作对切割复数的影响，并研究了各种图族（包括树、循环、完整多方图和棱柱[math]）的可壳性、同调类型和同调。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.