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Toric Rings and Ideals of Stable Set Polytopes

Author

Listed:
  • Kazunori Matsuda

    (Faculty of Engineering, Kitami Institute of Technology, Kitami, Hokkaido 090-8507, Japan)

  • Hidefumi Ohsugi

    (Department of Mathematical Sciences, School of Science and Technology, Kwansei Gakuin University, Sanda, Hyogo 669-1337, Japan)

  • Kazuki Shibata

    (Department of Mathematics, College of Science, Rikkyo University, Toshima-ku, Tokyo 171-8501, Japan)

Abstract

In the present paper, we study the normality of the toric rings of stable set polytopes, generators of toric ideals of stable set polytopes, and their Gröbner bases via the notion of edge polytopes of finite nonsimple graphs and the results on their toric ideals. In particular, we give a criterion for the normality of the toric ring of the stable set polytope and a graph-theoretical characterization of the set of generators of the toric ideal of the stable set polytope for a graph of stability number two. As an application, we provide an infinite family of stable set polytopes whose toric ideal is generated by quadratic binomials and has no quadratic Gröbner bases.

Suggested Citation

  • Kazunori Matsuda & Hidefumi Ohsugi & Kazuki Shibata, 2019. "Toric Rings and Ideals of Stable Set Polytopes," Mathematics, MDPI, vol. 7(7), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:613-:d:247320
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