Related papers: Directed Graph Minors and Serial-Parallel Width
Path-addition is an operation that takes a graph and adds an internally vertex-disjoint path between two vertices together with a set of supplementary edges. Path-additions are just the opposite of taking minors. We show that some classes…
We introduce a new arc in directed graphs of integers. Among other things, we determine the positive integers that have arcs to all except a finite number of positive integers. We also propose some possible research problems at the end of…
Given a connected graph $G(V, E)$, the edge dimension, denoted $\mathrm{edim}(G)$, is the least size of a set $S \subseteq V$ that distinguishes every pair of edges of $G$, in the sense that the edges have pairwise distinct tuples of…
In this paper we introduce the linear clique-width, linear NLC-width, neighbourhood-width, and linear rank-width for directed graphs. We compare these parameters with each other as well as with the previously defined parameters directed…
Graph embedding techniques are pivotal in real-world machine learning tasks that operate on graph-structured data, such as social recommendation and protein structure modeling. Embeddings are mostly performed on the node level for learning…
A directed graph is semi-transitive if and only if it is acyclic and for any directed path $u_1\rightarrow u_2\rightarrow \cdots \rightarrow u_t$, $t \geq 2$, either there is no edge from $u_1$ to $u_t$ or all edges $u_i\rightarrow u_j$…
A graph $H$ is said to be an induced minor of a graph $G$ if $H$ can be obtained from $G$ by a sequence of vertex deletions and edge contractions. Equivalently, $H$ is an induced minor of $G$ if there exists an induced minor model of $H$ in…
Learning the structure of causal directed acyclic graphs (DAGs) is useful in many areas of machine learning and artificial intelligence, with wide applications. However, in the high-dimensional setting, it is challenging to obtain good…
We present a method to generate directed acyclic graphs (DAGs) using deep reinforcement learning, specifically deep Q-learning. Generating graphs with specified structures is an important and challenging task in various application fields,…
Treewidth on undirected graphs is known to have many algorithmic applications. When considering directed width-measures there are much less results on their deployment for algorithmic results. In 2022 the first author, Rabinovich and…
Let $G=(V,E)$ be a connected graph, let $v\in V$ be a vertex and let $e=uw\in E$ be an edge. The distance between the vertex $v$ and the edge $e$ is given by $d_G(e,v)=\min\{d_G(u,v),d_G(w,v)\}$. A vertex $w\in V$ distinguishes two edges…
We look at a graph property called reducibility which is closely related to a condition developed by Brown to evaluate Feynman integrals. We show for graphs with a fixed number of external momenta, that reducibility with respect to both…
A \emph{three-dimensional grid drawing} of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight line segments representing the edges do not cross. Our aim is to produce three-dimensional…
A two-terminal graph is a simple graph equipped with two distinguished vertices, called terminals. Let $T_{n,m}$ be the class consisting of all nonisomorphic two-terminal graphs on $n$ vertices and $m$ edges. Let $G$ be any two-terminal…
This paper endeavors to learn time-varying graphs by using structured temporal priors that assume underlying relations between arbitrary two graphs in the graph sequence. Different from many existing chain structure based methods in which…
It is well-known that in finite graphs, large complete minors/topological minors can be forced by assuming a large average degree. Our aim is to extend this fact to infinite graphs. For this, we generalise the notion of the relative end…
This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.…
In Pe\~na (2007), MCMC sampling is applied to approximately calculate the ratio of essential graphs (EGs) to directed acyclic graphs (DAGs) for up to 20 nodes. In the present paper, we extend that work from 20 to 31 nodes. We also extend…
A well-studied challenge that arises in the structure learning problem of causal directed acyclic graphs (DAG) is that using observational data, one can only learn the graph up to a "Markov equivalence class" (MEC). The remaining undirected…
In multivariate statistics, acyclic mixed graphs with directed and bidirected edges are widely used for compact representation of dependence structures that can arise in the presence of hidden (i.e., latent or unobserved) variables. Indeed,…