In this paper, we obtain a combinatorial formula for computing the Betti numbers in the linear strand of edge ideals of bipartite Kneser graphs. We deduce lower and upper bounds for regularity of powers of edge ideals of these graphs in terms of associated combinatorial data and show that the lower bound is attained in some cases. Also, we obtain bounds on the projective dimension of edge ideals of these graphs in terms of combinatorial data.

中文翻译：

---

二部kneser图的某些同调不变量

在本文中，我们获得了一个组合公式，用于计算二部 Kneser 图的边理想线性链中的 Betti 数。我们根据相关的组合数据推断出这些图的边缘理想幂的规律性的下限和上限，并表明在某些情况下达到了下限。此外，我们根据组合数据获得了这些图的边缘理想的投影维度的界限。