相关论文: Diamond-free Degree Sequences

In Boij-Soderberg theory, it is known that for any degree sequence $\mathbf{d}$, there exists a finitely generated module that has a pure resolution of type $\mathbf{d}$. On the other hand, in the case of ideal, there are two necessary…

The Maximum Weight Independent Set (MWIS) Problem on graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum total weight. Being one of the most investigated and most important problems on graphs, it is well…

Let $I$ be a monomial ideal in the polynomial ring $S$ generated by elements of degree at most $d$. In this paper, it is shown that, if the $i$-th syzygy of $I$ has no element of degrees $j, \ldots, j+(d-1)$ (where $j \geq i+d$), then…

Uniform sampling of simple graphs having a given degree sequence is a known problem with exponential complexity in the square of the mean degree. For undirected graphs, randomised approximation algorithms have nonetheless been shown to…

The degree sequence of a graph is a numerical method to characterize the properties of graphs. Generalized forms of degree sequences exist for complete graphs and complete graphs. Nikolopolus et al. characterized the number of spanning…

We address the degree-diameter problem for Cayley graphs of Abelian groups (Abelian graphs), both directed and undirected. The problem turns out to be closely related to the problem of finding efficient lattice coverings of Euclidean space…

In the Maximum Independent Set problem we are asked to find a set of pairwise nonadjacent vertices in a given graph with the maximum possible cardinality. In general graphs, this classical problem is known to be NP-hard and hard to…

In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for…

We address the problem of semi-supervised learning in relational networks, networks in which nodes are entities and links are the relationships or interactions between them. Typically this problem is confounded with the problem of…

In this paper, we introduce the \emph{interval query problem} on cube-free median graphs. Let $G$ be a cube-free median graph and $\mathcal{S}$ be a commutative semigroup. For each vertex $v$ in $G$, we are given an element $p(v)$ in…

We consider problems of finding a maximum size/weight $t$-matching without forbidden subgraphs in an undirected graph $G$ with the maximum degree bounded by $t+1$, where $t$ is an integer greater than $2$. Depending on the variant forbidden…

We introduce a procedure, called the Degree Sequence Index Strategy (DSI), by which to bound graph invariants by certain indices in the ordered degree sequence. As an illustration of the DSI strategy, we show how it can be used to give new…

Learning the dependence structure among variables in complex systems is a central problem across medical, natural, and social sciences. These structures can be naturally represented by graphs, and the task of inferring such graphs from data…

Novel dynamic programming algorithms to count the set $D(n)$ of zero-free degree sequences of length $n$, the set $D_c(n)$ of degree sequences of connected graphs on $n$ vertices and the set $D_b(n)$ of degree sequences of biconnected…

Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved superior performance in tasks such as node classification. However, analyzing heterogeneous graph of different types of nodes and links…

The question of whether 3-Coloring can be solved in polynomial-time for the diameter two graphs is a well-known open problem in the area of algorithmic graph theory. We study the problem restricted to graph classes that avoid cycles of…

We prove that the class of $(K_t,sP_1+P_5)$-free graphs has bounded mim-width for every $s\geq 0$ and $t\geq 1$, and that there is a polynomial-time algorithm that, given a graph in the class, computes a branch decomposition of constant…

Dense subgraph discovery methods are routinely used in a variety of applications including the identification of a team of skilled individuals for collaboration from a social network. However, when the network's node set is associated with…

We address here the problem of generating random graphs uniformly from the set of simple connected graphs having a prescribed degree sequence. Our goal is to provide an algorithm designed for practical use both because of its ability to…

Covariate-dependent graph learning has gained increasing interest in the graphical modeling literature for the analysis of heterogeneous data. This task, however, poses challenges to modeling, computational efficiency, and interpretability.…