Related papers: cliquematch: Finding correspondence via cliques in…
This paper proposes a new algorithm for solving maximal cliques for simple undirected graphs using the theory of prime numbers. A novel approach using prime numbers is used to find cliques and ends with a discussion of the algorithm.
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 graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…
A \emph{clique} is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for the following graph classes: (1) graphs with $n$ vertices and $m$ edges; (2) graphs with $n$ vertices, $m$ edges,…
I present a single algorithm which solves the clique problems, "What is the largest size clique?", "What are all the maximal cliques?" and the decision problem, "Does a clique of size k exist?" for any given graph in polynomial time. The…
Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of…
Quasi-cliques are dense incomplete subgraphs of a graph that generalize the notion of cliques. Enumerating quasi-cliques from a graph is a robust way to detect densely connected structures with applications to bio-informatics and social…
Ray intersection graphs are intersection graphs of rays, or halflines, in the plane. We show that any planar graph has an even subdivision whose complement is a ray intersection graph. The construction can be done in polynomial time and…
In this paper, we provide polynomial-time algorithms for different extensions of the matching counting problem, namely maximal matchings, path matchings (linear forest) and paths, on graph classes of bounded clique-width. For maximal…
The problem of maximising the number of cliques among $n$-vertex graphs from various graph classes has received considerable attention. We investigate this problem for the class of $1$-planar graphs where we determine precisely the maximum…
Quantum adiabatic evolution provides a general technique for the solution of combinatorial search problems on quantum computers. We present the results of a numerical study of a particular application of quantum adiabatic evolution, the…
The maximal clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry,…
A strong clique in a graph is a clique intersecting every maximal independent set. We study the computational complexity of six algorithmic decision problems related to strong cliques in graphs and almost completely determine their…
In a random intersection graph $G_{n,m,p}$, each of $n$ vertices selects a random subset of a set of $m$ labels by including each label independently with probability $p$ and edges are drawn between vertices that have at least one label in…
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…
A novel approach to complex problems has been previously applied to graph classification and the graph equivalence problem. Here we apply it to the NP complete problem of finding the largest perfect clique within a graph $G$.
We consider the enumeration of maximal bipartite cliques (bicliques) from a large graph, a task central to many practical data mining problems in social network analysis and bioinformatics. We present novel parallel algorithms for the…
A cocomparability graph is a graph whose complement admits a transitive orientation. An interval graph is the intersection graph of a family of intervals on the real line. In this paper we investigate the relationships between interval and…
There are many methods to find a maximum (or maximal) clique in large networks. Due to the nature of combinatorics, computation becomes exponentially expensive as the number of vertices in a graph increases. Thus, there is a need for…
Multiple interval graphs are variants of interval graphs where instead of a single interval, each vertex is assigned a set of intervals on the real line. We study the complexity of the MAXIMUM CLIQUE problem in several classes of multiple…