Revista de la
Unión Matemática Argentina
Binomial edge ideals of cographs
Thomas Kahle and Jonas Krüsemann
Volume 63, no. 2 (2022), pp. 305–316    

https://doi.org/10.33044/revuma.2247

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Abstract

We determine the Castelnuovo–Mumford regularity of binomial edge ideals of complement-reducible graphs (cographs). For cographs with $n$ vertices the maximum regularity grows as $2n/3$. We also bound the regularity by graph-theoretic invariants and construct a family of counterexamples to a conjecture of Hibi and Matsuda.

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