scispace - formally typeset
Journal ArticleDOI

On cliques in graphs

J. W. Moon, +1 more
- 01 Mar 1965 - 
- Vol. 3, Iss: 1, pp 23-28
Reads0
Chats0
TLDR
In this article, the maximum number of cliques possible in a graph with n nodes is determined and bounds are obtained for the number of different sizes of clique possible in such a graph.
Abstract
A clique is a maximal complete subgraph of a graph. The maximum number of cliques possible in a graph withn nodes is determined. Also, bounds are obtained for the number of different sizes of cliques possible in such a graph.

read more

Citations
More filters
Posted Content

Extremal problems related to Betti numbers of flag complexes

TL;DR: In this paper, an upper bound of 1.32^n for the sum of Betti numbers of any n-vertex flag complex and 1.25 √ n for the independence complex of a triangle-free graph was shown.
Journal ArticleDOI

Exact Polynomial-time Algorithm for the Clique Problem and P = NP for Clique Problem

TL;DR: It has been found that the Minimum Nil Sweeper Algorithm is not applicable to Clique problem for all undirected graphs which was previously claimed.
Journal ArticleDOI

Detecting Cliques Using Degree and Connectivity Constraints

TL;DR: This paper introduces pruning strategies, by which linear time algorithm for detecting clique is obtained, which has wide application in bioinformatics and graph mining.
Journal ArticleDOI

Counting and enumerating independent sets with applications to combinatorial optimization problems

TL;DR: Methods to count and enumerate maximal/maximum independent sets in threshold graphs and k -threshold graphs are introduced and improved and can be applied to combinatorial optimization problems, and in particular to different variations of the knapsack problem.
Journal ArticleDOI

The Problems of Transition Predicates Construction in Hierarchical Concurrent Controllers

TL;DR: The paper presents a problem of a transition predicates construction in hierarchical concurrent state oriented notation and suggests some statecharts syntactic structures solving these problems.
References
More filters
Journal ArticleDOI

On the theory of graphs

Related Papers (5)