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Nonvanishing Betti numbers of edge ideals of weakly chordal graphs

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Abstract

We show that Kimura’s necessary and sufficient condition for the nonvanishingness of multigraded Betti numbers of edge ideals of chordal graphs can be extended to the larger family of weakly chordal graphs. We also obtain a description for the Betti numbers of edge ideals of threshold graphs in terms of the Euler characteristic of the independence complex of its induced subgraphs.

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Acknowledgements

The authors thank the referees for their useful comments and suggestions which substantially improved the exposition of the paper.

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  1. Departamento de Matemáticas, Cinvestav-IPN, A.P. 14-740, 07360, Mexico, CDMX, Mexico

    José Martínez-Bernal, Oscar A. Pizá-Morales & Miguel A. Valencia-Bucio

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  1. José Martínez-Bernal
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  2. Oscar A. Pizá-Morales
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  3. Miguel A. Valencia-Bucio
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Correspondence to José Martínez-Bernal.

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José Martínez-Bernal was supported by SNI México. Oscar A. Pizá-Morales and Miguel A. Valencia-Bucio were supported by CONACyT México.

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Martínez-Bernal, J., Pizá-Morales, O.A. & Valencia-Bucio, M.A. Nonvanishing Betti numbers of edge ideals of weakly chordal graphs. J Algebr Comb 58, 279–290 (2023). https://doi.org/10.1007/s10801-023-01248-0

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