Geodesic
Regularity of powers of binomial edge ideals of complete multipartite graphs
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 793-810

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Let $G=K_{n_1,n_2,\ldots ,n_r}$ be a complete multipartite graph on $[n]$ with $n>r>1$ and $J_G$ being its binomial edge ideal. It is proved that the Castelnuovo-Mumford regularity ${\rm reg}(J^t_G)$ is $2t+1$ for any positive integer $t$.
DOI : 10.21136/CMJ.2023.0246-22
Classification : 05E40, 13D02
Keywords: Castelnuovo-Mumford regularity; binomial edge ideal; multipartite graph 
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Wang, Hong; Tang, Zhongming. Regularity of powers of binomial edge ideals of complete multipartite graphs. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 793-810. doi: 10.21136/CMJ.2023.0246-22

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