Related papers: Edge rings of bipartite graphs with linear resolut…
In the present paper, we give a complete classification of connected simple graphs whose edge rings have a $q$-linear resolution with $q \geq 2$. In particular, we show that the edge ring of a finite connected simple graph with a $q$-linear…
It is shown that the edge ring of a finite connected simple graph with a $3$-linear resolution is a hypersurface.
We provide a characterisation of all graphs whose parity binomial edge ideals have pure resolutions. In particular, we show that the minimal free resolution of a parity binomial edge ideal is pure if and only if the corresponding graph is a…
In [{Structural properties and decomposition of linear balanced matrices}, {\it Mathematical Programming}, 55:129--168, 1992], Conforti and Rao conjectured that every balanced bipartite graph contains an edge that is not the unique chord of…
We explicitly describe cellular minimal free resolutions of certain classes of edge ideals of weighted complete bipartite graphs based on a construction of Visscher. Specifically, we show that Visscher's construction minimally resolves all…
Edge polytopes is a class of interesting polytope with rich algebraic and combinatorial properties, which was introduced by Ohsugi and Hibi. In this papar, we follow a previous study on cutting edge polytopes by Hibi, Li and Zhang. Instead…
In [7], Higashitani, Kummer, and Micha{\l}ek pose a conjecture about the symmetric edge polytopes of complete multipartite graphs and confirm it for a number of families in the bipartite case. We confirm that conjecture for a number of new…
We study minimal free resolutions of edge ideals of bipartite graphs. We associate a directed graph to a bipartite graph whose edge ideal is unmixed, and give expressions for the regularity and the depth of the edge ideal in terms of…
Let G be an arbitrary simple graph. The main results are explicit representations of the edge cone of G as a finite intersection of closed halfspaces. If G is bipartite and connected we determine the facets of the edge cone and present a…
Symmetric edge polytopes of graphs are important object in Ehrhart theory,and have an application to Kuramoto models. In the present paper, we study the upper and lower bounds for the number of facets of symmetric edge polytopes of…
Let $G$ be a simple graph on $n$ vertices and $\mathcal{I}_G$ denotes parity binomial edge ideal of $G$ in the polynomial ring $S = \mathbb{K}[x_1,\ldots, x_n, y_1, \ldots, y_n].$ We obtain a lower bound for the regularity of parity…
We introduce a new class of algebras arising from graphs, called binomial edge rings. Given a graph $G$ on $d$ vertices with $n$ edges, the binomial edge ring of $G$ is defined to be the subalgebra of the polynomial ring with $2d$ variables…
We characterize all graphs whose binomial edge ideals have pure resolutions. Moreover, we introduce a new switching of graphs which does not change some algebraic invariants of graphs, and using this, we study the linear strand of the…
For a graph $G=(V,E)$ the edge ring $k[G]$ is $k[x_1,\ldots,x_n]/I(G)$, where $n=|V|$ and $I(G)$ is generated by $\{ x_ix_j;\{ i,j\}\in E\}$. The conjecture we treat is the following. If $k[G]$ has a 2-linear resolution, then the projective…
Given a finite connected bipartite graph, finite-dimensional indecomposable semisimple Leibniz algebras are constructed. Furthermore, any finite-dimensional indecomposable semisimple Leibniz algebra admits a similar construction.
In this paper we consider a natural extremal graph theoretic problem of topological sort, concerning the minimization of the (topological) connectedness of the independence complex of graphs in terms of its dimension. We observe that the…
We focus in this paper on edge ideals associated to bipartite graphs and give a combinatorial characterization of those having regularity 3. When the regularity is strictly bigger than 3, we determine the first step $i$ in the minimal…
Let k, p, q be positive integers with k < p < q+1. We prove that the maximum spectral radius of a simple bipartite graph obtained from the complete bipartite graph Kp,q of bipartition orders p and q by deleting k edges is attained when the…
A strong edge coloring of a graph $G$ is a proper edge coloring in which each color class is an induced matching of $G$. In 1993, Brualdi and Quinn Massey proposed a conjecture that every bipartite graph without $4$-cycles and with the…
A combinatorial criterion for the edge ring of a finite connected graph to satisfy Serre's condition R_1 is studied.