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Acta Mathematica Vietnamica

, Volume 41, Issue 1, pp 69–76 | Cite as

Strongly Koszul Edge Rings

  • Takayuki Hibi
  • Kazunori Matsuda
  • Hidefumi Ohsugi
Article

Abstract

We classify the finite connected simple graphs whose edge rings are strongly Koszul. From the classification, it follows that if the edge ring is strongly Koszul, then its toric ideal possesses a quadratic Gröbner basis.

Keywords

Strongly Koszul algebra Finite graph Edge ring 

Mathematics Subject Classification (2010)

13P20 16S37 

Notes

Acknowledgments

This research was supported by the JST (Japan Science and Technology Agency) CREST (Core Research for Evolutional Science and Technology) research project Harmony of Gröbner Bases and the Modern Industrial Society in the framework of the JST Mathematics Program “Alliance for Breakthrough between Mathematics and Sciences.”

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2014

Authors and Affiliations

  • Takayuki Hibi
    • 1
  • Kazunori Matsuda
    • 2
  • Hidefumi Ohsugi
    • 2
    • 3
  1. 1.Department of Pure and Applied Mathematics, Graduate School of Information Science and TechnologyOsaka UniversityOsakaJapan
  2. 2.Department of Mathematics, College of ScienceRikkyo UniversityTokyoJapan
  3. 3.Department of Mathematical Sciences, School of Science and TechnologyKwansei Gakuin UniversityHyogoJapan

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