Cohen-Macaulay binomial edge ideals of cactus graphs

We classify the Cohen-Macaulay binomial edge ideals of cactus and bicyclic graphs

Cohen-Macaulay binomial edge ideals of small deviation

We classify all binomial edge ideals that are complete intersection and Cohen-Macaulay almost complete intersection. We also describe an algorithm and provide an implementation to compute primary decomposition of binomial edge ideals.Comment: 8 pages, 1 figur

Extremal Betti numbers of some Cohen-Macaulay binomial edge ideals

We provide the regularity and the Cohen-Macaulay type of binomial edge ideals of Cohen-Macaulay cones, and we show the extremal Betti numbers of some classes of Cohen-Macaulay binomial edge ideals: Cohen-Macaulay bipartite and fan graphs. In addition, we compute the Hilbert-Poincar\'e series of the binomial edge ideals of some Cohen-Macaulay bipartite graphs

Closed graphs are proper interval graphs

In this note we prove that every closed graph $G$ is up to isomorphism a proper interval graph. As a consequence we obtain that there exist linear-time algorithms for closed graph recognition.Comment: 7 page

2-dimensional vertex decomposable circulant graphs

Let $G$ be the circulant graph $C_n(S)$ with $S\subseteq\{ 1,\ldots,\left \lfloor\frac{n}{2}\right \rfloor\}$ and let $\Delta$ be its independence complex. We describe the well-covered circulant graphs with 2-dimensional $\Delta$ and construct an infinite family of vertex-decomposable circulant graphs within this family

On the reduced Euler characteristic of independence complexes of circulant graphs

Let $G$ be the circulant graph $C_n(S)$ with $S\subseteq\{ 1,\ldots,\left \lfloor\frac{n}{2}\right \rfloor\}$. We study the reduced Euler characteristic $\tilde{\chi}$ of the independence complex $\Delta (G)$ for $n=p^k$ with $p$ prime and for $n=2p^k$ with $p$ odd prime, proving that in both cases $\tilde{\chi}$ does not vanish. We also give an example of circulant graph whose independence complex has $\tilde{\chi}$ equals to $0$, giving a negative answer to R. Hoshino

On the extremal Betti numbers of binomial edge ideals of block graphs

We compute one of the distinguished extremal Betti number of the binomial edge ideal of a block graph, and classify all block graphs admitting precisely one extremal Betti number

Some algebraic invariants of mixed product ideals

We compute some algebraic invariants (e.g. depth, Castelnuovo - Mumford regularity) for a special class of monomial ideals, namely the ideals of mixed products. As a consequence, we characterize the Cohen-Macaulay ideals of mixed products

Construction of Cohen-Macaulay binomial edge ideals

We discuss algebraic and homological properties of binomial edge ideals associated to graphs which are obtained by gluing of subgraphs and the formation of cones.Comment: 13 pages, 2 figure

Krull dimension and regularity of binomial edge ideals of block graphs

We give a lower bound for the Castelnuovo-Mumford regularity of binomial edge ideals of block graphs by computing the two distinguished extremal Betti numbers of a new family of block graphs, called flower graphs. Moreover, we present a linear time algorithm to compute the Castelnuovo-Mumford regularity and Krull dimension of binomial edge ideals of block graphs.Comment: Accepted in Journal of Algebra and Applicatio