Related papers: Local Certification of Some Geometric Intersection…
A graph $G=(V,E)$ is a geometric intersection graph if every node $v \in V$ is identified with a geometric object of some particular type, and two nodes are adjacent if the corresponding objects intersect. Geometric intersection graph…
The goal of local certification is to locally convince the vertices of a graph $G$ that $G$ satisfies a given property. A prover assigns short certificates to the vertices of the graph, then the vertices are allowed to check their…
Local certification consists in assigning labels to the nodes of a network to certify that some given property is satisfied, in such a way that the labels can be checked locally. In the last few years, certification of graph classes…
A proof labelling scheme for a graph class $\mathcal{C}$ is an assignment of certificates to the vertices of any graph in the class $\mathcal{C}$, such that upon reading its certificate and the certificates of its neighbors, every vertex…
Detecting specific structures in a network has been a very active theme of research in distributed computing for at least a decade. In this paper, we start the study of subgraph detection from the perspective of local certification.…
The graph model checking problem consists in testing whether an input graph satisfies a given logical formula. In this paper, we study this problem in a distributed setting, namely local certification. The goal is to assign labels to the…
Intersection graphs are very important in both theoretical as well as application point of view. Depending on the geometrical representation, different type of intersection graphs are defined. Among them interval, circular-arc, permutation,…
We present compact distributed interactive proofs for the recognition of two important graph classes, well-studied in the context of centralized algorithms, namely complement reducible graphs and distance-hereditary graphs. Complement…
We study graph classes modeled by families of non-crossing (NC) connected sets. Two classic graph classes in this context are disk graphs and proper interval graphs. We focus on the cases when the sets are paths and the host is a tree…
Grid intersection graphs are the intersection graphs of vertical and horizontal segments in the plane. When the bottom and respectively left endpoints of the vertical and horizontals segments belong to a line with negative slope, the graph…
We unify several seemingly different graph and digraph classes under one umbrella. These classes are all broadly speaking different generalizations of interval graphs, and include, in addition to interval graphs, also adjusted interval…
A distributed graph algorithm is basically an algorithm where every node of a graph can look at its neighborhood at some distance in the graph and chose its output. As distributed environment are subject to faults, an important issue is to…
Local certification is a topic originating from distributed computing, where a prover tries to convince the vertices of a graph $G$ that $G$ satisfies some property $\mathcal{P}$. To convince the vertices, the prover gives a small piece of…
We investigate graphs that can be represented as vertex intersections of horizontal and vertical paths in a grid, the so called $B_0$-VPG graphs. Recognizing this class is an NP-complete problem. Although, there exists a polynomial time…
In this paper, we present a 2-local proof labeling scheme with labels in $\{ 0,1,2\}$ for leader election in anonymous meshed graphs. Meshed graphs form a general class of graphs defined by a distance condition. They comprise several…
A circular-arc graph is the intersection graph of arcs of a circle. It is a well-studied graph model with numerous natural applications. A certifying algorithm is an algorithm that outputs a certificate, along with its answer (be it…
The most elusive problem around the class of circular-arc graphs is identifying all minimal graphs that are not in this class. The main obstacle is the lack of a systematic way of enumerating these minimal graphs. McConnell [FOCS 2001]…
In local certification, vertices of a $n$-vertex graph perform a local verification to check if a given property is satisfied by the graph. This verification is performed thanks to certificates, which are pieces of information that are…
This paper deals with local certification, specifically locally checkable proofs: given a graph property, the task is to certify whether a graph satisfies the property. The verification of this certification needs to be done locally without…
A graph is locally chordal if each of its small-radius balls is chordal. In an earlier work [AKK25], the authors and Kobler proved that locally chordal graphs can be characterized by having chordal local covers, by forbidding short cycles…