Related papers: A Novel Approach Applied to the Largest Clique Pro…
Finding a maximum clique in a given graph is one of the fundamental NP-hard problems. We compare two multi-core thread-parallel adaptations of a state-of-the-art branch and bound algorithm for the maximum clique problem, and provide a novel…
A clique transversal in a graph is a set of vertices intersecting all maximal cliques. The problem of determining the minimum size of a clique transversal has received considerable attention in the literature. In this paper, we initiate the…
We analyze the problem of identifying large cliques in graphs that are affected by adversarial uncertainty. More specifically, we consider a new formulation, namely the adversarial maximum clique problem, which extends the classical…
Determining the existence of $k$-clique in the arbitrary graph is one of the NP problems. We suggest a novel way to determine the existence of $k$-clique in the clique complex $G$ under specific conditions, by using the normal mode and…
The maximum clique problem (MCP) is to find the largest complete subgraph in an undirected graph, that is, the subgraph in which there are edges between every two different vertices. It is an NP-Hard problem with wide applications,…
Deep neural networks have been applied to a wide range of problems across different application domains with great success. Recently, research into combinatorial optimization problems in particular has generated much interest in the machine…
A complete graph is the graph in which every two vertices are adjacent. For a graph $G=(V,E)$, the complete width of $G$ is the minimum $k$ such that there exist $k$ independent sets $\mathtt{N}_i\subseteq V$, $1\le i\le k$, such that the…
A $k$-defective clique of an undirected graph $G$ is a subset of its vertices that induces a nearly complete graph with a maximum of $k$ missing edges. The maximum $k$-defective clique problem, which asks for the largest $k$-defective…
The maximum labelled clique problem is a variant of the maximum clique problem where edges in the graph are given labels, and we are not allowed to use more than a certain number of distinct labels in a solution. We introduce a new…
This contribution extends the Bron Kerbosch algorithm for solving the maximum weight clique problem, where continuous-valued weights are assigned to both, vertices and edges. We applied the proposed algorithm to graph matching problems.
This paper formulates a necessary and sufficient condition for a generic graph matching problem to be equivalent to the maximum vertex and edge weight clique problem in a derived association graph. The consequences of this results are…
The maximum clique problem (MCP) is a fundamental problem in graph theory and in computational complexity. Given a graph G, the problem is that of finding the largest clique (complete subgraph) in G. The MCP has many important applications…
As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…
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…
We propose improved exact and heuristic algorithms for solving the maximum weight clique problem, a well-known problem in graph theory with many applications. Our algorithms interleave successful techniques from related work with novel data…
The maximal clique enumeration (MCE) problem has numerous applications in biology, chemistry, sociology, and graph modeling. Though this problem is well studied, most current research focuses on finding solutions in large sparse graphs or…
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…
It is well-known that the graph isomorphism problem can be posed as an equivalent problem of determining whether an auxiliary graph structure contains a clique of specific order. However, the algorithms that have been developed so far for…
Finding maximum cliques in large networks is a challenging combinatorial problem with many real-world applications. We present a fast algorithm to achieve the exact solution for the maximum clique problem in large sparse networks based on…
We propose a fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks. The method exhibits a roughly linear runtime scaling over real-world networks…