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In graph coloring problems, the goal is to assign a positive integer color to each vertex of an input graph such that adjacent vertices do not receive the same color assignment. For classic graph coloring, the goal is to minimize the…
The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, information retrieval and many other areas related to the World Wide Web. There exist several algorithms for the problem with…
A hedge graph is a graph whose edge set has been partitioned into groups called hedges. Here we consider a generalization of the well-known \textsc{Cluster Deletion} problem, named \textsc{Hedge Cluster Deletion}. The task is to compute the…
Graph neural networks (GNNs) are widely used for learning node embeddings in graphs, typically adopting a message-passing scheme. This approach, however, leads to the neighbor explosion problem, with exponentially growing computational and…
We consider the problem of finding a subgraph of a given graph which minimizes the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already when all functions are the same, we show that it…
Many real-world networks can be modeled as graphs. Finding dense subgraphs is a key problem in graph mining with applications in diverse domains. In this paper, we consider two variants of the densest subgraph problem where multiple graph…
Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class…
Given a property (graph class) $\Pi$, a graph $G$, and an integer $k$, the \emph{$\Pi$-completion} problem consists in deciding whether we can turn $G$ into a graph with the property $\Pi$ by adding at most $k$ edges to $G$. The…
The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…
We consider a pursuit-evasion game that describes the process of extinguishing a fire burning on the nodes of an undirected graph. We denote the minimum number of firefighters required by ffn(G) and provide almost sharp bounds to this graph…
Arboricity is a graph parameter akin to chromatic number, in that it seeks to partition the vertices into the smallest number of sparse subgraphs. Where for the chromatic number we are partitioning the vertices into independent sets, for…
Roughly speaking, gerrymandering is the systematic manipulation of the boundaries of electoral districts to make a specific (political) party win as many districts as possible. While typically studied from a geographical point of view,…
In the area of beyond-planar graphs, i.e. graphs that can be drawn with some local restrictions on the edge crossings, the recognition problem is prominent next to the density question for the different graph classes. For 1-planar graphs,…
This paper investigates the computational complexity of deciding whether the vertices of a graph can be partitioned into a disjoint union of cliques and a triangle-free subgraph. This problem is known to be $\NP$-complete on arbitrary…
Graph similarity computation is one of the core operations in many graph-based applications, such as graph similarity search, graph database analysis, graph clustering, etc. Since computing the exact distance/similarity between two graphs…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
Simplifying graphs is a very applicable problem in numerous domains, especially in computational geometry. Given a geometric graph and a threshold, the minimum-complexity graph simplification asks for computing an alternative graph of…
The K-way vertex cut problem} consists in, given a graph G, finding a subset of vertices of a given size, whose removal partitions G into the maximum number of connected components. This problem has many applications in several areas. It…
An injective $k$-edge-coloring of a graph $G$ is an assignment of colors, i.e. integers in $\{1, \ldots , k\}$, to the edges of $G$ such that any two edges each incident with one distinct endpoint of a third edge, receive distinct colors.…
The widely studied edge modification problems ask how to minimally alter a graph to satisfy certain structural properties. In this paper, we introduce and study a new edge modification problem centered around transforming a given graph into…