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Certain Homological Invariants of Bipartite Kneser Graphs

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arxiv 2105.06144 v1 pith:IAHTT4RZ submitted 2021-05-13 math.AC math.CO

Certain Homological Invariants of Bipartite Kneser Graphs

Ajay Kumar , Pavinder Singh , Rohit Verma This is my paper
classification math.AC math.CO
keywords graphscombinatorialedgeidealsbipartiteboundsdatakneser
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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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