Journal of Algebra and Its Applications· 2026Q2
A note on toric ideals of graphs and Knutson-Miller-Yong Decompositions
- 0citations
- Q2SCImago
- 2026year
Short summary
A Gröbner basis technique reveals connections between graph properties and algebraic properties of their toric ideals, including a new way to detect bipartite graph deletions and bounds on chromatic numbers.
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Key points
- A Gröbner basis technique is used to link graph properties with toric ideals.
- An algebraic method is presented to detect bipartite graph deletions.
- Bounds for the chromatic number of a graph are derived from its initial ideal.
AI-generated from the title and abstract; the full text is not read.
Abstract
We use a Gröbner basis technique first introduced by Knutson, Miller and Yong to study the interplay between properties of a graph [Formula: see text] and algebraic properties of the toric ideal that it defines. We first recover a well-known height formula for the toric ideal of a graph [Formula: see text] and demonstrate an algebraic property that can detect when a graph deletion is bipartite. We also bound the chromatic number [Formula: see text] using information about an initial ideal of [Formula: see text].
The authors' abstract, as published at the source. Journal of Algebra and Its Applications, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics