Related papers: A balanced non-partitionable Cohen-Macaulay comple…
A conjecture of Fan and Raspaud [3] asserts that every bridgeless cubic graph con-tains three perfect matchings with empty intersection. Kaiser and Raspaud [6] sug-gested a possible approach to this problem based on the concept of a…
In this paper, a theorem is proved that generalizes several existing amalgamation results in various ways. The main aim is to disentangle a given edge-colored amalgamated graph so that the result is a graph in which the edges are shared out…
We prove convergence to equilibrium for a class of coagulation-fragmentation equations that do not satisfy a detailed balance condition. More precisely, we consider perturbations of constant rate kernels. Our result provides in particular…
Let $\mathcal{C}$ be a clutter with a perfect matching $e_1,...,e_g$ of K\"onig type and let $\Delta_\mathcal{C}$ be the Stanley-Reisner complex of the edge ideal of $\mathcal{C}$. If all c-minors of $\mathcal{C}$ have a free vertex and…
We give a minimum degree condition sufficent to ensure the existence of a fractional $K_r$-decomposition in a balanced $r$-partite graph (subject to some further simple necessary conditions). This generalises the non-partite problem studied…
We extend a reciprocity theorem of Stanley about enumeration of integer points in polyhedral cones when one exchanges strict and weak inequalities. The proof highlights the roles played by Cohen-Macaulayness and canonical modules. The…
In 1994, it was conjectured by Fan and Raspaud that every simple bridgeless cubic graph has three perfect matchings whose intersection is empty. In this paper we answer a question recently proposed by Mkrtchyan and Vardanyan, by giving an…
We study the independence complexes of families of well-covered circulant graphs discovered by Boros-Gurvich-Milani\v{c}, Brown-Hoshino, and Moussi. Because these graphs are well-covered, their independence complexes are pure simplicial…
Via the BGG correspondence a simplicial complex Delta on [n] is transformed into a complex of coherent sheaves on P^n-1. We show that this complex reduces to a coherent sheaf F exactly when the Alexander dual Delta^* is Cohen-Macaulay. We…
In this paper we introduce a class of polygonal complexes for which we can define a notion of sectional combinatorial curvature. These complexes can be viewed as generalizations of 2-dimensional Euclidean and hyperbolic buildings. We focus…
Extensions of the notions of polynomially and rationally convex hulls are introduced. Using these notions, a generalization of a result of Duval and Levenberg on polynomially convex hulls containing no analytic discs is presented. As a…
In an earlier work [K. Castillo et al., J. Math. Anal. Appl., 514 (2022) 126358], we give positive answer to the first, and apparently more easy, part of a conjecture of M. Ismail concerning the characterization of the continuous $q$-Jacobi…
In this paper, we study a conjecture of Andries E. Brouwer from 1996 regarding the minimum number of vertices of a strongly regular graph whose removal disconnects the graph into non-singleton components. We show that strongly regular…
We introduce a strengthening of the notion of transience for planar maps in order to relax the standard condition of bounded degree appearing in various results, in particular, the existence of Dirichlet harmonic functions proved by…
The non-Gorenstein locus of stable set rings of finite simple perfect graphs is studied. We describe combinatorially those perfect graphs whose stable set rings are Gorenstein on the punctured spectrum. In addition, we show that, in…
In this note, we give some necessary conditions for an $r$-partite graph such that the edge ring of the graph is Cohen-Macaulay. It is proved that if $G$ is an $r$-partite Cohen-Macaulay graph which is covered by some disjoint cliques of…
Let $H$ be a simple undirected graph. The family of all matchings of $H$ forms a simplicial complex called the matching complex of $H$. Here , we give a classification of all graphs with a Gorenstein matching complex. Also we study when the…
Doran, Jensen and Giansiracusa showed a bijection between homogeneous elements in the Cox ring of $\overline{M}_{0,n}$ not divisible by any exceptional divisor section, and weighted pure-dimensional simplicial complexes satisfying a…
Recently, Milani\v{c} and Trotignon introduced the class of equistarable graphs as graphs without isolated vertices admitting positive weights on the edges such that a subset of edges is of total weight $1$ if and only if it forms a maximal…
Noting a curious link between Andrews' even-odd crank and the Stanley rank, we adopt a combinatorial approach building on the map of conjugation and continue the study of integer partitions with parts separated by parity. Our motivation is…