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Induced matchings in strongly biconvex graphs and some algebraic applications
Sara Saeedi Madani, Dariush Kiani
In this paper, motivated by a question posed in \cite{AH}, we introduce strongly biconvex graphs as a subclass of weakly chordal and bipartite graphs. We give a linear time algorit…
Binomial edge ideals of regularity
Sara Saeedi Madani, Dariush Kiani
Let be the binomial edge ideal of a graph . We characterize all graphs whose binomial edge ideals, as well as their initial ideals, have regularity . Consequently we ch…
Some Cohen-Macaulay and unmixed binomial edge ideals
Dariush Kiani, Sara Saeedi Madani
We study unmixed and Cohen-Macaulay properties of the binomial edge ideal of some classes of graphs. We compute the depth of the binomial edge ideal of a generalized block graph. W…
The Castelnuovo-Mumford regularity of binomial edge ideals
Dariush Kiani, Sara Saeedi Madani
We prove a conjectured upper bound for the Castelnuovo-Mumford regularity of binomial edge ideals of graphs, due to Matsuda and Murai. Indeed, we prove that $\mathrm{reg}(J_G)\leq…