A note on toric ideals of graphs and Knutson-Miller-Yong decompositions

Fuente: arXiv
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Autori principali: Da Silva, Sergio, Naguit, Emma, Rajchgot, Jenna
Natura: Preprint
Pubblicazione: 2025
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author Da Silva, Sergio
Naguit, Emma
Rajchgot, Jenna
author_facet Da Silva, Sergio
Naguit, Emma
Rajchgot, Jenna
contents We use a Gröbner basis technique first introduced by Knutson, Miller and Yong to study the interplay between properties of a graph $G$ 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 $I_G$ and demonstrate an algebraic property that can detect when a graph deletion is bipartite. We also bound the chromatic number $χ(G)$ using information about an initial ideal of $I_G$.
format Preprint
id arxiv_https___arxiv_org_abs_2502_08069
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A note on toric ideals of graphs and Knutson-Miller-Yong decompositions
Da Silva, Sergio
Naguit, Emma
Rajchgot, Jenna
Commutative Algebra
Combinatorics
13P10, 14M25, 05C15, 05E40, 05C25
We use a Gröbner basis technique first introduced by Knutson, Miller and Yong to study the interplay between properties of a graph $G$ 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 $I_G$ and demonstrate an algebraic property that can detect when a graph deletion is bipartite. We also bound the chromatic number $χ(G)$ using information about an initial ideal of $I_G$.
title A note on toric ideals of graphs and Knutson-Miller-Yong decompositions
topic Commutative Algebra
Combinatorics
13P10, 14M25, 05C15, 05E40, 05C25
url https://arxiv.org/abs/2502.08069