Regularity of binomial edge ideals of chordal graphs

• Rouzbahani Malayeri, Mohammad ^[1] ; Saeedi Madani, Sara ^[1] ; Kiani, Dariush ^[1]
  1. [1] Amirkabir University of Technology

     Amirkabir University of Technology

     Irán

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 72, Fasc. 2, 2021, págs. 411-422
• Idioma: inglés
• DOI: 10.1007/s13348-020-00293-3
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• Resumen

  • In this paper we prove the conjectured upper bound for Castelnuovo–Mumford regularity of binomial edge ideals posed in [23], in the case of chordal graphs. Indeed, we show that the regularity of any chordal graph G is bounded above by the number of maximal cliques of G, denoted by c(G). Moreover, we classify all chordal graphs G for which \mathcal {L}(G)=c(G), where \mathcal {L}(G) is the sum of the lengths of longest induced paths of connected components of G. We call such graphs strong interval graphs. We show that the regularity of a strong interval graph G coincides with \mathcal {L}(G) as well as c(G).