Toricness of Binomial Edge Ideals
Mahdis Saeedi, Farhad Rahmati, Seyyede Masoome Seyyedi
TL;DR
This paper characterizes when the binomial edge ideal of a graph is toric, showing it occurs precisely when each connected component is complete, and relates it to sums of toric ideals of bipartite complete graphs.
Contribution
It provides a complete characterization of toric binomial edge ideals in terms of graph connectivity and completeness, linking them to bipartite complete graphs.
Findings
Binomial edge ideal is toric iff each component is complete.
Toric binomial edge ideals are sums of ideals from bipartite complete graphs.
Characterization connects graph structure to algebraic properties.
Abstract
Let G be a finite simple graph. In this paper we will show that the binomial edge ideal of G, JG is toric if and only if each connected component of G is complete and in this case it is the sum of toric ideal associated to bipartite complete graphs.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic Geometry and Number Theory