论文标题
图形的总切割复合物
Total Cut Complexes of Graphs
论文作者
论文摘要
受Fröberg（1990）和Eagon and Reiner（1998）的启发，我们定义了图$ g $的\ emph {总$ k $ -cut Complex}，这是简单的综合体，其刻画是$ g $中$ k $的独立尺寸$ k $的补充。我们使用代数拓扑和离散莫尔斯理论的技术研究了各种图形族的总切割复合物的同质类型和组合性能，包括弦图，周期，两部分图，Prism $ k_n \ times k_2 $和网格图。
Inspired by work of Fröberg (1990), and Eagon and Reiner (1998), we define the \emph{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.
