A Little … there is an NP complete problem, 3-SAT for one, that reduces to CLIQUE in polynomial time. Clique is a fundamental concept in graph theory. Given a Graph, find if it can be divided into two C . Part (b) above is fine-- all over in every resource and very well explained. Prudhvi Varma Penmetcha Clique. So, this page describes an idea that can make searching for a maximum clique much faster for very dense graphs. Introduction. Code Review Stack Exchange is a question and answer site for peer programmer code reviews. A Clique in an undirected graph G = (V,E) is a subset of the vertex set C ⊆ V, such that for every two vertices in C, there exists an edge connecting the two. Contents List of Figuresv Using These Notesxi Chapter 1.

Maximum Clique: A Clique of the largest possible size in a given graph. The CLIQUE problem-- problem of finding the maximum clique in a graph is NP-complete.

Part 2. above is fine -- all over in every resource and very well explained. Ask Question Asked 3 years, 11 months ago. 1. The exact maximum clique problem Recently I needed the size of the largest coclique in a number of sparse graphs (or, equivalently, the size of the largest clique in a number of dense graphs) and found that my old algorithm was 50 times as fast as published algorithms. A Clique is a subgraph of graph such that all vertcies in subgraph are completely connected with each other. That is, CLIQUE is . a.) Find a vertex v of the smallest possible degree in G. If the degree of v is n − 1, stop; G is a clique, so the largest clique in G has size n. Otherwise, remove v and all of its edges from G. Find the largest clique in the smaller graph. Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Home ; Questions ; Tags ; Users ; Unanswered ; Maximum clique problem: fast heuristic. To find a clique of G: Suppose that G has n vertices. in NP and ; there is an NP complete problem, 3-SAT for one, that reduces to CLIQUE in polynomial time. Graph Theory: Penn State Math 485 Lecture Notes Version 1.4.3 Christopher Gri n « 2011-2017 Licensed under aCreative Commons Attribution-Noncommercial-Share Alike 3.0 United States License With Contributions By: Suraj Shekhar. Preface and Introduction to Graph Theory1 1. in NP and b.) The CLIQUE problem -- problem of finding the maximum clique in a graph -- is NP-complete. Maximal Clique: A Clique that cannot be extended by including one more adjacent vertex. This paper proposes an efficient heuristic approach for finding maximum clique using minimal independent set in a graph. Given a Graph, find if it can be divided into two C. A Clique is a subgraph of graph such that all vertcies in subgraph are completely connected with each other. Sign up to join this community. A maximum clique is a maximum collection of objects which are mutually related in some specified criterion. Some History of Graph Theory and Its Branches1 2. It only takes a minute to sign up. That is, CLIQUE is.