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Summer 2022 On regularity bounds and linear resolutions of toric algebras of graphs
Rimpa Nandi, Ramakrishna Nanduri
J. Commut. Algebra 14(2): 285-296 (Summer 2022). DOI: 10.1216/jca.2022.14.285

Abstract

Let G be a simple graph. We show that if G is connected and R(I (G)) is normal, reg(R(I (G)))α0 (G), where α0 (G) is the vertex cover number of G. As a consequence, for every normal König connected graph G, reg(R(I (G)))= mat (G), the matching number of G. For a gap-free graph G, we give various combinatorial upper bounds for reg(R(I (G))). As a consequence we give various sufficient conditions for the equality of reg(R(I (G))) and mat (G). Finally we show that if G is a chordal graph such that K[G] has q-linear resolution (q4), then K[G] is a hypersurface, which proves the conjecture of Hibi, Matsuda and Tsuchiya [10, Conjecture 0.2] affirmatively for chordal graphs.

Citation

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Rimpa Nandi. Ramakrishna Nanduri. "On regularity bounds and linear resolutions of toric algebras of graphs." J. Commut. Algebra 14 (2) 285 - 296, Summer 2022. https://doi.org/10.1216/jca.2022.14.285

Information

Received: 31 October 2019; Accepted: 24 December 2019; Published: Summer 2022
First available in Project Euclid: 14 July 2022

Digital Object Identifier: 10.1216/jca.2022.14.285

Subjects:
Primary: 05E40 , 13D02 , 13H10
Secondary: 52B20

Keywords: Castelnuovo–Mumford regularity , chordal graph , gap-free graphs , Rees algebra , regularity , resolution , toric algebra

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.14 • No. 2 • Summer 2022
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