论文标题
图形及其同质类型的较高独立复合物
Higher Independence Complexes of graphs and their homotopy types
论文作者
论文摘要
对于$ r \ geq 1 $，图$ g $的$ r $独立复合体是一个简单的综合体，其面部为子集$ i \ subseteq v（g）$，使得诱导子级$ g [i] $的每个组件最多具有$ r $ $ $ pertices。在本文中，我们确定了某些图的$ r $独立络合物的同质类型，包括完整的$ s $明确图，完全搅拌的图形，周期图和完美的$ M $ $ - $ - yr-ary树。在每种情况下，这些复合物要么是对等维球的楔形物的同型，要么是可缩度的。我们还为它们的同质副本类型提供了封闭式公式。
For $r\geq 1$, the $r$-independence complex of a graph $G$ is a simplicial complex whose faces are subset $I \subseteq V(G)$ such that each component of the induced subgraph $G[I]$ has at most $r$ vertices. In this article, we determine the homotopy type of $r$-independence complexes of certain families of graphs including complete $s$-partite graphs, fully whiskered graphs, cycle graphs and perfect $m$-ary trees. In each case, these complexes are either homotopic to a wedge of equi-dimensional spheres or are contractible. We also give a closed form formula for their homotopy types.
