Total Cut Complexes of Graphs

IF 0.6 3区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Discrete & Computational Geometry Pub Date : 2024-02-22 DOI:10.1007/s00454-024-00630-4

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

引用次数: 0

Abstract

Inspired by work of Fröberg (1990), and Eagon and Reiner (1998), we define the total k-cut complex of a graph G to be the simplicial complex whose facets are the complements of independent sets of size k in G. We study the homotopy types and combinatorial properties of total cut complexes for various families of graphs, including chordal graphs, cycles, bipartite graphs, the prism \(K_n \times K_2\), and grid graphs, using techniques from algebraic topology and discrete Morse theory.

Abstract Image

查看原文本刊更多论文

图形的总切复数

受 Fröberg (1990) 以及 Eagon 和 Reiner (1998) 工作的启发，我们将图 G 的总 k 切复合体定义为简单复合体，其切面是 G 中大小为 k 的独立集的补集。我们利用代数拓扑学和离散莫尔斯理论中的技术，研究了各种图系的全切复数的同调类型和组合性质，包括弦图、循环图、双分图、棱柱图（K_n \times K_2\）和网格图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Discrete & Computational Geometry 数学-计算机：理论方法

CiteScore

1.80

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Discrete & Computational Geometry (DCG) is an international journal of mathematics and computer science, covering a broad range of topics in which geometry plays a fundamental role. It publishes papers on such topics as configurations and arrangements, spatial subdivision, packing, covering, and tiling, geometric complexity, polytopes, point location, geometric probability, geometric range searching, combinatorial and computational topology, probabilistic techniques in computational geometry, geometric graphs, geometry of numbers, and motion planning.