Two cliques of genes identified computationally for their high co-expression in the mouse brain according to the Allen Brain Atlas, and for their enrichment in genes related to autism spectrum disorder, have recently been shown to be highly co-expressed in the cerebellar cortex, compared to what could be expected by chance. Moreover, the expression of these cliques of genes is not homogeneous a...

This conjecture was proven in 1985 by Vojtech Rodl[4]. It will be convenient for us to formulate the Erd}os-Hanani conjecture in hypergraph terms. Let G be the complete l-graph on n points. Then m(n; k; l) is the maximal number of disjoint k-cliques that may be packed into G, and M(n; k; l) is the minimal number of k-cliques that cover G. The proof of R odl was remarkable on several levels. I...

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.

Our main result essentially reduces the problem of finding an edge-decomposition of a balanced r-partite graph of large minimum degree into r-cliques to the problem of finding a fractional r-clique decomposition or an approximate one. Together with very recent results of Bowditch and Dukes as well as Montgomery on fractional decompositions into triangles and cliques respectively, this gives the...

By using the concepts of ant imetry and n-chain it is possible to define and to investigate some properties of connectivity in a sociometric group. I t is shown tha t tbe number of elements in a group, the number of antimetries, and the degree of connectivity must satisfy certain inequalities. Using the ideas of connectivity, a generalized concept of clique, called an n-clique, is introduced. n...

A graph class has few cliques if there is a polynomial bound on the number of maximal cliques contained in any member of the class. This restriction is equivalent to the requirement that any graph in the class has a polynomial sized intersection representation that satisfies the Helly property. On any such class of graphs some problems that are NP-complete on general graphs, such as the maximum...