Related papers: Deciding first-order properties of nowhere dense g…

A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…

The present paper is the first one in the sequence of papers about a simple class of {\em framed $4$-graphs}; the goal of the present paper is to collect some well-known results on planarity and to reformulate them in the language of {\em…

Graph neural networks (GNNs) are a powerful tool to learn representations on graphs by iteratively aggregating features from node neighbourhoods. Many variant models have been proposed, but there is limited understanding on both how to…

An ordering of the vertices of a graph is \emph{connected} if every vertex (but the first) has a neighbor among its predecessors. The greedy colouring algorithm of a graph with a connected order consists in taking the vertices in order, and…

Temporal graphs provide a useful model for many real-world networks. Unfortunately the majority of algorithmic problems we might consider on such graphs are intractable. There has been recent progress in defining structural parameters which…

For a finite collection of graphs ${\cal F}$, the \textsc{${\cal F}$-TM-Deletion} problem has as input an $n$-vertex graph $G$ and an integer $k$ and asks whether there exists a set $S \subseteq V(G)$ with $|S| \leq k$ such that $G…

Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…

We prove that a minimal automaton has a minimal adjacency matrix rank and a minimal adjacency matrix nullity using equitable partition (from graph spectra theory) and Nerode partition (from automata theory). This result naturally introduces…

We contribute an approach to the problem of locally computing sparse connected subgraphs of dense graphs. In this setting, given an edge in a connected graph $G = (V, E)$, an algorithm locally decides its membership in a sparse connected…

We show that for every fixed undirected graph $H$, there is a $O(|V(G)|^3)$ time algorithm that tests, given a graph $G$, if $G$ contains $H$ as a topological subgraph (that is, a subdivision of $H$ is subgraph of $G$). This shows that…

We prove that if $G$ is a sparse graph --- it belongs to a fixed class of bounded expansion $\mathcal{C}$ --- and $d\in \mathbb{N}$ is fixed, then the $d$th power of $G$ can be partitioned into cliques so that contracting each of these…

While previous works have shown that an overwhelming number of scale-free networks are sparse, there still exist some real-world networks including social networks, urban networks, information networks, which are by observation dense. In…

We show that for any fixed dense graph G and bounded-degree tree T on the same number of vertices, a modest random perturbation of G will typically contain a copy of T . This combines the viewpoints of the well-studied problems of embedding…

We propose a local-to-global strategy for graph machine learning and network analysis by defining certain local features and vector representations of nodes and then using them to learn globally defined metrics and properties of the nodes…

A graph class $\mathcal C$ is monadically dependent if one cannot interpret all graphs in colored graphs from $\mathcal C$ using a fixed first-order interpretation. We prove that monadically dependent classes can be exactly characterized by…

We study the class of 1-perfectly orientable graphs, that is, graphs having an orientation in which every out-neighborhood induces a tournament. 1-perfectly orientable graphs form a common generalization of chordal graphs and circular arc…

Network data can be conveniently modeled as a graph signal, where data values are assigned to the nodes of a graph describing the underlying network topology. Successful learning from network data requires methods that effectively exploit…

A graph property P is said to be testable if one can check if a graph is close or far from satisfying P using few random local inspections. Property P is said to be non-deterministically testable if one can supply a "certificate" to the…

For every $q\in \mathbb N$ let $\textrm{FO}_q$ denote the class of sentences of first-order logic FO of quantifier rank at most $q$. If a graph property can be defined in $\textrm{FO}_q$, then it can be decided in time $O(n^q)$. Thus,…

We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random with replacement. These matrices have a one-to-one correspondence with the…