Margaret Bayer, Mark Denker, Marija Jelić Milutinović, Rowan Rowlands, Sheila Sundaram, Lei Xue
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引用次数: 0
摘要
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。
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.
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