Related papers: Distributed Interactive Proofs for the Recognition…
A simple-triangle graph (also known as a PI graph) is the intersection graph of a family of triangles defined by a point on a horizontal line and an interval on another horizontal line. The recognition problem for simple-triangle graphs was…
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…
Graph coloring is fundamental to distributed computing. We give the first general treatment of the coloring of virtual graphs, where the graph $H$ to be colored is locally embedded within the communication graph $G$. Besides generalizing…
Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely…
A graph $G$ is called self-ordered (a.k.a asymmetric) if the identity permutation is its only automorphism. Equivalently, there is a unique isomorphism from $G$ to any graph that is isomorphic to $G$. We say that $G=(V,E)$ is robustly…
Graph convolution (GConv) is a widely used technique that has been demonstrated to be extremely effective for graph learning applications, most notably node categorization. On the other hand, many GConv-based models do not quantify the…
Circular-arc graphs are intersection graphs of arcs on the circle. The aim of our work is to present a polynomial time algorithm testing whether two circular-arc graphs are isomorphic. To accomplish our task we construct decomposition…
A labelling of a graph is an assignment of labels to its vertex or edge sets (or both), subject to certain conditions, a well established concept. A labelling of a graph G of order n is termed a numbering when the set of integers {1,...,n}…
The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the…
Let $G$ be a finite group. The intersection graph of $G$ is a graph whose vertex set is the set of all proper non-trivial subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $H\cap K \neq \{e\}$, where $e$ is…
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. These graphs and their generalizations were applied in various fields, including modeling channel routing…
The intersection graph of a group $G$ is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of $G$, and there is an edge between two distinct vertices $H$…
Intersection graphs of geometric objects have been extensively studied, both due to their interesting structure and their numerous applications; prominent examples include interval graphs and permutation graphs. In this paper we study a…
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…
Many techniques for the automated verification of distributed protocols have been developed over the past several years, but their performance is still unpredictable and their failure modes can be opaque for industrial scale verification…
A graph $G=(V,E)$ is a pairwise compatibility graph (PCG) if there exists an edge-weighted tree $T$ and two non-negative real numbers $d_{min}$ and $d_{max}$, $d_{min} \leq d_{max}$, such that each node $u \in V$ is uniquely associated to a…
An injective coloring of a given graph G = (V, E) is a vertex coloring of G such that any two vertices with common neighbor receive distinct colors. An e-injective coloring of a graph G is a vertex coloring of G such that any two vertices…
This paper deals with graph classes characterization and recognition. A popular way to characterize a graph class is to list a minimal set of forbidden induced subgraphs. Unfortunately this strategy usually does not lead to an efficient…
In this paper, we focus on graph class identification problems in the population protocol model. A graph class identification problem aims to decide whether a given communication graph is in the desired class (e.g. whether the given…
Graphs derived from groups are a widely studied class of graphs, motivated by their highly symmetric structure. In particular, G-graphs offer an easy and interesting alternative construction of semi-symmetric graphs. After recalling the…