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This work introduces a novel algorithm for finding the connected components of a graph where the vertices and edges are grouped into sets defining a Set--Based Graph. The algorithm, under certain restrictions on those sets, has the…
The graph bisection problem is the problem of partitioning the vertex set of a graph into two sets of given sizes such that the sum of weights of edges joining these two sets is optimized. We present a semidefinite programming relaxation…
Say that an edge of a graph G dominates itself and every other edge adjacent to it. An edge dominating set of a graph G = (V,E) is a subset of edges E' of E which dominates all edges of G. In particular, if every edge of G is dominated by…
Temporal graphs arise when modeling interactions that evolve over time. They usually come in several flavors, depending on the number of parameters used to describe the temporal aspects of the interactions: time of appearance, duration,…
The website reductions.network serves as a comprehensive database for exploring problems and reductions between them. It presents several complexity classes in the form of an interconnected graph where problems are represented as vertices,…
Let $G=(V,E)$ be a graph. A set $S\subseteq V(G)$ is a dominating set, if every vertex in $V(G)\backslash S$ is adjacent to at least one vertex in $S$. The $k$-dominating graph of $G$, $D_k (G)$, is defined to be the graph whose vertices…
The core vertex set of a graph is an invariant of the graph. It consists of those vertices associated with the non-zero entries of the nullspace vectors of a $\{0,1\}$-adjacency matrix. The remaining vertices of the graph form the…
Graph Neural Networks (GNNs) have emerged as an efficient alternative to convolutional approaches for vision tasks such as image classification, leveraging patch-based representations instead of raw pixels. These methods construct graphs…
A dominating set D in a graph G is a subset of its vertices such that every vertex of the graph which does not belong to set D is adjacent to at least one vertex from set D. A set of vertices of graph G is a global dominating set if it is a…
A pendant vertex is one of degree one and an isolated vertex has degree zero. A neighborhood star-free (NSF for short) graph is one in which every vertex is contained in a triangle except pendant vertices and isolated vertices. This class…
The visibility graph of a simple polygon represents visibility relations between its vertices. Knowing the correct order of the vertices around the boundary of a polygon and its visibility graph, it is an open problem to locate the vertices…
We introduce a family of graph parameters, called induced multipartite graph parameters, and study their computational complexity. First, we consider the following decision problem: an instance is an induced multipartite graph parameter $p$…
In a labeling scheme the vertices of a given graph from a particular class are assigned short labels such that adjacency can be algorithmically determined from these labels. A representation of a graph from that class is given by the set of…
We consider the problem of determining the maximum induced density of a graph H in any graph on n vertices. The limit of this density as n tends to infinity is called the inducibility of H. The exact value of this quantity is known only for…
Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…
Proximity graphs have been studied for several decades, motivated by applications in computational geometry, geography, data mining, and many other fields. However, the computational complexity of classic graph problems on proximity graphs…
Let $G=(V(G),E(G))$ be a simple graph. A non-empty set $S\subseteq V (G)$ is a weakly connected dominating set in $G$, if the subgraph obtained from $G$ by removing all edges each joining any two vertices in $V (G)\setminus S$ is connected.…
We study the recently introduced problem of finding dense common subgraphs: Given a sequence of graphs that share the same vertex set, the goal is to find a subset of vertices $S$ that maximizes some aggregate measure of the density of the…
The complexity of visual stimuli plays an important role in many cognitive phenomena, including attention, engagement, memorability, time perception and aesthetic evaluation. Despite its importance, complexity is poorly understood and…
A visibility algorithm maps time series into complex networks following a simple criterion. The resulting visibility graph has recently proven to be a powerful tool for time series analysis. However its straightforward computation is…