Bipartite graphs whose edge algebras are complete intersections

Details Bipartite graphs whose edge algebras are complete intersections Bipartite graphs whose edge algebras are complete intersections

2002-09-25

arxiv.org/abs/math/0209348v1

Journal of Algebra, 220 (1999) pp. 519-530

Mathematics

Commutative Algebra

Scientific paper

Let R be monomial sub-algebra of $k[x_1,...,x_N]$ generated by square free monomials of degree two. This paper addresses the following question: when is R a complete intersection? For such a k-algebra we can associate a graph G whose vertices are $x_1,...,x_N$ and whose edges are $\{(x_i, x_j) | x_i x_j \in R \}$. Conversely, for any graph G with vertices $\{x_1,...,x_N\}$ we define the {\it edge algebra associated with G} as the sub-algebra of $k[x_1,...,x_N]$ generated by the monomials ${x_i x_j | (x_i,x_j) \text{is an edge of} G}$. We denote this monomial algebra by k[G]. This paper describes all bipartite graphs whose edge algebras are complete intersections.

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