198 research outputs found
The regularity of binomial edge ideals of graphs
In this paper, we study the Castelnuovo-Mumford regularity and the graded Betti numbers of the binomial edge ideals of some classes of graphs. Our special attention is devoted to a conjecture which asserts that the number of maximal cliques of a graph provides an upper bound for the regularity of its binomial edge ideal
The regularity of binomial edge ideals of graphs
We prove two recent conjectures on some upper bounds for the
Castelnuovo-Mumford regularity of the binomial edge ideals of some different
classes of graphs. We prove the conjecture of Matsuda and Murai for graphs
which has a cut edge or a simplicial vertex, and hence for chordal graphs. We
determine the regularity of the binomial edge ideal of the join of graphs in
terms of the regularity of the original graphs, and consequently prove the
conjecture of Matsuda and Murai for such a graph, and hence for complete
-partite graphs. We also generalize some results of Schenzel and Zafar about
complete -partite graphs. We also prove the conjecture due to the authors
for a class of chordal graphs.Comment: 11 pages, 1 figur
Local cohomology of binomial edge ideals and their generic initial ideals
We provide a Hochster type formula for the local cohomology modules of binomial edge ideals. As a consequence we obtain a simple criterion for the CohenâMacaulayness and Buchsbaumness of these ideals and we describe their CastelnuovoâMumford regularity and their Hilbert series. Conca and Varbaro (Square-free Groebner degenerations, 2018) have recently proved a conjecture of Conca, De Negri and Gorla (J Comb Algebra 2:231â257, 2018) relating the graded components of the local cohomology modules of CartwrightâSturmfels ideals and their generic initial ideals. We provide an alternative proof for the case of binomial edge idealsPeer ReviewedPostprint (author's final draft
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