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arXiv · 2105.06144

Certain Homological Invariants of Bipartite Kneser Graphs

Ajay Kumar·Pavinder Singh·Rohit Verma
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Abstract

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.

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Ajay Kumar, Pavinder Singh, Rohit Verma. 2021-05-13. Certain Homological Invariants of Bipartite Kneser Graphs. https://arxiv.org/abs/2105.06144

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