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SUMMARY:Christos Tatakis (University of Western Macedonia)
DTSTART:20250508T120000Z
DTEND:20250508T130000Z
DTSTAMP:20260423T021336Z
UID:GANT/75
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GANT/75/">To
 ric ideals of graphs minimally generated by a Grοbner basis</a>\nby Chris
 tos Tatakis (University of Western Macedonia) as part of Greek Algebra & N
 umber Theory Seminar\n\n\nAbstract\nThe problem of describing families of 
 ideals minimally generated by either one or all of its Grobner bases is a 
 central topic in commutative algebra. This work tackles this problem in th
 e context of toric ideals of graphs. We call a graph G an MG-graph if its 
 toric ideal IG is minimally generated by a Grobner basis\, while we say th
 at G is an UMG-graph if every reduced Grobner  basis of IG is a minimal ge
 nerating set. We prove that G is an UMG-graph if and only if IG is a gener
 alized robust ideal\, i.e. ideal whose universal Grobner  ̈ basis and uni
 versal Markov basis coincide. We observe that the class of MG-graphs is no
 t closed under taking subgraphs\, and we prove that it is hereditary (i.e.
 \, closed under taking induced subgraphs). Also\, we describe two families
  of bipartite MG-graphs: ring graphs and graphs whose induced cycles have 
 the same length. The latter extends a result of Ohsugi and Hibi\, which co
 rresponds to graphs whose induced cycles have all length 4 (joint work wit
 h Ignacio Garcia-Marco and Irene Marquez-Corbella).\n
LOCATION:https://researchseminars.org/talk/GANT/75/
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