Graphs and Ideals Generated by Some 2-Minors

By Masahiro Ohtani. 2009

200 citations recorded by the source corpus.

Let G be a finite graph on [n] = {1, 2,…, n}, X a 2 × n matrix of indeterminates over a field K, and S = K[X] a polynomial ring over K. In this article, we study about ideals I G of S generated by 2-minors [i, j] of X which correspond to edges {i, j} of G. In particular, we construct a Gröbner basis of I G as a set of paths of G and compute a primary decomposition.

Subfields: Algebra and Number Theory, Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/e6059f75de69d86111aae0853f1821290860ad24

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Citations in the corpus

Cohen-Macaulay binomial edge ideals (2010, background): “They appear ind ependently, and at about the same time, also in the paper [6].”
Regularity bounds for binomial edge ideals (2012, background): “[4] and Ohtani [6], is the ideal in the polynomial ring S = K[x1, .”
Construction of Cohen–Macaulay Binomial Edge Ideals (2012, background): “is a Gröbner bases of JG′ (see [6] and [9]).”
On the regularity of binomial edge ideals (2013, background): “Binomial edge ideals were introduced in [7] and [9].”
Some Cohen–Macaulay and Unmixed Binomial Edge Ideals (2015, background): “The binomial edge ideal of a graph was introduced, at about the same time, in [5] and [8].”