Huge and expensive computation resources are usually required to perform graph labelling at high speed. This fact restricts an extensive use of this methodology in industrial applications such as visual inspection. A new systolic architecture is presented which computes structural distances between cliques of different graphs based on a modified incremental Levenshtein distance algorithm. The d...

an Numbers Sean McGuinness University of Ume a September, 1994 Abstract. In this paper, we show that for p 4 if C is a clique decomposition obtained by removing maximal cliques(ie. their edges) of order at least p one by one until none remain, in which case the remaining edges are removed one by one, then the sum of the orders of the cliques in C is at most 2tp 1(n): Here tp 1(n) denotes the nu...

In this paper we define the notion of a compatibility relation so as to have a common framework for three nonmonotonic reasoning systems: normal logic programming, extended logic programming, and a restricted form of default logic. We show some properties of the maximal cliques of the pair-wise compatibility graph givn by the relation between the rules of the various reasoning systems. Properti...

In this paper we calculate the average number of cliques in random scale-free networks. We consider first the hidden variable ensemble and subsequently the Molloy Reed ensemble. In both cases we find that cliques, i.e. fully connected subgraphs, appear also when the average degree is finite. This is in contrast to what happens in Erdös and Renyi graphs in which diverging average degree is requi...

We characterize clique trees of a chordal graph in their relation to simplicial vertices and perfect sequences of maximal cliques. We investigate boundary cliques defined by Shibata[23] and clarify their relation to endpoints of clique trees. Next we define a symmetric binary relation between the set of clique trees and the set of perfect sequences of maximal cliques. We describe the relation a...

Minimal triangulations and potential maximal cliques are the main ingredients for a number of polynomial time algorithms on different graph classes computing the treewidth of a graph. Potential maximal cliques are also the main engine of the fastest so far exact (exponential) treewidth algorithm. Based on the recent results of Mazoit, we define the structures that can be regarded as minimal tri...

A greedy clique decomposition of a graph is obtained by removing maximal cliques from a graph one by one until the graph is empty. We have recently shown that any greedy clique decomposition of a graph of order n has at most-~ cliques. A greedy max-clique decomposition is a particular kind of greedy clique decomposition where maximum cliques are removed, instead of just maximal ones. In this pa...

A bilevel image can be modeled by the Markov random field (MRF). Let G = (V,E) be an 8-connected graph, where V and E denote the nodes (vertices) and edges, modeling the pixels and the connectivities in an image, respectively. The MRF with 2-point cliques is defined on the 8-connected graph. The 2-point cliques consist of horizontal, vertical and diagonal neighboring nodes (Figure 1a). A node i...

re chromosomes distributed randomly within the cell nucleus during interphase, or do they preferentially cluster into specific groups? On page 237, Cornforth et al. address this question, which has been debated vigorously for nearly a century, and conclude that the distribution of chromosomes within the nucleus of human cells is mostly, but not entirely, random. The work provides the most compr...

Many graph mining applications rely on detecting subgraphs which are large near-cliques. There exists a dichotomy between the results in the existing work related to this problem: on the one hand formulations that are geared towards finding large near-cliques are NP-hard and frequently inapproximable due to connections with the Maximum Clique problem. On the other hand, the densest subgraph pro...