Related papers: Double Threshold Digraphs
We prove that the order of an ordered group is an interval order if and only if it is a semiorder. Next, we prove that every semiorder is isomorphic to a collection $\mathcal J$ of intervals of some totally ordered abelian group, these…
If $G$ is a graph and $\vec H$ is an oriented graph, we write $G\to \vec H$ to say that every orientation of the edges of $G$ contains $\vec H$ as a subdigraph. We consider the case in which $G=G(n,p)$, the binomial random graph. We…
Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…
Given two elements $x,y$ of a semigroup $X$ we write $x\lesssim y$ if for every homomorphism $\chi:X\to\{0,1\}$ we have $\chi(x)\le\chi(y)$. The quasiorder $\lesssim$ is called the $binary$ $quasiorder$ on $X$. It induces the equivalence…
We investigate the fine-grained and the parameterized complexity of several generalizations of binary constraint satisfaction problems (BINARY-CSPs), that subsume variants of graph colouring problems. Our starting point is the observation…
Standard decision theory seeks conditions under which a preference relation can be compressed into a single real-valued function. However, when preferences are incomplete or intransitive, a single function fails to capture the agent's…
For some geometric graph classes, tractability of testing first-order formulas is precisely characterised by the graph parameter twin-width. This was first proved for interval graphs among others in [BCKKLT, IPEC '22], where the equivalence…
Recently, graph neural networks have attracted great attention and achieved prominent performance in various research fields. Most of those algorithms have assumed pairwise relationships of objects of interest. However, in many real…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…
Semialgebraic graphs are graphs whose vertices are points in $\mathbb{R}^d$, and adjacency between two vertices is determined by the truth value of a semialgebraic predicate of constant complexity. We show how to harness polynomial…
Graphical models have proven to be powerful tools for representing high-dimensional systems of random variables. One example of such a model is the undirected graph, in which lack of an edge represents conditional independence between two…
In this paper, we introduce the notion of two-way $(t,\lambda)$-liking digraphs as a way to extend the results for generalized friendship graphs. A two-way $(t,\lambda)$-liking digraph is a digraph in which every $t$ vertices have exactly…
Bilateral agreement based random undirected graphs were introduced and analyzed by La and Kabkab in 2015. The construction of the graph with $n$ vertices in this model uses a (random) preference order on other $n-1$ vertices and each vertex…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a…
Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an…
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This subclass of perfect graphs has been extensively studied, due to both its interesting structure…
We study bipartite graphs partially ordered by the induced subgraph relation. Our goal is to distinguish classes of bipartite graphs which are or are not well-quasi-ordered (wqo) by this relation. Answering an open question from…
Binary classification is one of the most common problem in machine learning. It consists in predicting whether a given element belongs to a particular class. In this paper, a new algorithm for binary classification is proposed using a…
Here in particular, we give a characterization of Quasi-line Graphs in terms of forbidden induced subgraphs. In general, we prove a necessary and sufficient condition for a graph to be a union of two cliques.