The bandwidth of a graph is the labeling of vertices with minimum maximum edge difference. For many graph families this is NP-complete. A classic result computes the bandwidth for the hypercube. We generalize this result to give sharp lower bounds for products of cliques. This problem turns out to be equivalent to one in communication over multiple channels in which channels can fail and the in...

Many real-world datasets, such as biological networks and social networks, can be modeled as graphs. It is interesting to discover densely connected subgraphs from these graphs, as such subgraphs represent groups of objects sharing some common properties. Several algorithms have been proposed to mine quasi-cliques from undirected graphs, but they have not fully utilized the minimum degree const...

In this paper, we investigate the capabilities of Ant Colony Optimization (ACO) for solving the maximum clique problem. We describe Ant-Clique, an algorithm that successively generates maximal cliques through the repeated addition of vertices into partial cliques. ACO is used to choose, at each step, the vertex to add. We illustrate the behaviour of this algorithm on two representative benchmar...

Finding motifs in DNA sequences plays an important role in deciphering transcriptional regulatory mechanisms and drug target identification. In this paper, we propose an efficient algorithm, EDAM, for finding motifs based on frequency transformation and Minimum Bounding Rectangle (MBR) techniques. It works in three phases, frequency transformation, MBR-clique searching and motif discovery. In f...

Clustering applications dealing with perception based or biased data lead to models with non-disjunct clusters. There, objects to be clustered are allowed to belong to several clusters at the same time which results in a fuzzy clustering. It can be shown that this is equivalent to searching all maximal cliques in dynamic graphs like Gt = (V,Et), where Et−1 ⊂ Et, t = 1, . . . , T ;E0 = φ. In thi...

How to tell if a review is real or fake? What does the underworld of fraudulent reviewing look like? Detecting suspicious reviews has become a major issue for many online services. We propose the use of a clique-finding approach to discover well-organized suspicious reviewers. From a Yelp dataset with over one million reviews, we construct multiple Reviewer Similarity graphs to link users that ...

A graph G is coordinated if, for every induced subgraph H of G, the minimum number of colors that can be assigned to the cliques of H in such a way that no two cliques with non-empty intersection receive the same color is equal to the maximum number of cliques of H with a common vertex. In a previous work, coordinated graphs were characterized by minimal forbidden induced subgraphs within some ...

For r = 7, 8 we prove that if χ(G) = r, then cr(G) ≥ cr(Kr). The case r = 5 of the Weak Hajós Conjecture is equivalent to the Four Color Theorem, and the case r = 6 follows from a theorem of Oporowski and Zhao. We present partial results when r = 9.

A set of vertices is a dominating set in a graph if every vertex not in the dominating set is adjacent to one or more vertices in the dominating set. A dominating clique is a dominating set that induces a complete subgraph. Forbidden subgraph conditions sufficient to imply the existence of a dominating clique are given. For certain classes of graphs, a polynomial algorithm is given for finding ...

1. Introduction. Let 0 < p < 1 be fixed and denote by G a random graph with point set N, the set of natural numbers, such that each edge occurs with probability p, independently of all other edges. In other words the random variables ei5 , 1 < i < j, defined by _ 1 if (i, j) is an edge of G, et '-0 if (i, j) is not an edge of G, are independent r .v.'s with P(e i, = 1) = p, P(eij = 0) = 1-p. De...