Toric ideals associated with gap-free graphs

Alessio D'Alì ^[1]
1. [1] University of Genoa
  
  University of Genoa
  
  Genoa, Italia
Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 9 (September 2015), 2015, págs. 3862-3872
Idioma: inglés
DOI: 10.1016/j.jpaa.2014.12.025
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Resumen
- In this paper we prove that every toric ideal associated with a gap-free graph G has a squarefree lexicographic initial ideal. Moreover, in the particular case when the complementary graph of G is chordal (i.e. when the edge ideal of G has a linear resolution), we show that there exists a reduced Gröbner basis G of the toric ideal of G such that all the monomials in the support of G are squarefree. Finally, we show (using work by Herzog and Hibi) that if I is a monomial ideal generated in degree 2, then I has a linear resolution if and only if all powers of I have linear quotients, thus extending a result by Herzog, Hibi and Zheng.