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