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The maximum clique problem may be solved using as a subroutine an algorithm for the maximal clique listing problem, because the maximum clique must be included among all the maximal cliques. [ 17 ] In the k -clique problem, the input is an undirected graph and a number k .
In computer science, the clique problem is the computational problem of finding a maximum clique, or all cliques, in a given graph. It is NP-complete , one of Karp's 21 NP-complete problems . [ 6 ] It is also fixed-parameter intractable , and hard to approximate .
This algorithm was designed by Janez Konc and its description was published in 2007. [1] In comparison to earlier algorithms, MaxCliqueDyn has an improved coloring algorithm (ColorSort) and applies tighter, more computationally expensive upper bounds on a fraction of the search space. [1] Both improvements reduce time to find maximum clique.
A planted clique is a clique created from another graph by adding edges between all pairs of a selected subset of vertices. The planted clique problem can be formalized as a decision problem over a random distribution on graphs, parameterized by two numbers, n (the number of vertices), and k (the size of the clique).
A graph H is the clique graph K(G) of another graph if and only if there exists a collection C of cliques in H whose union covers all the edges of H, such that C forms a Helly family. This means that, if S is a subset of C with the property that every two members of S have a non-empty intersection, then S itself should also have a non-empty ...
The boy, born in 2005, and his family remained close with their former teacher and his parents allowed their sons and daughter to sleep over at Caron's house a couple nights a week, according to ABC6.
The clique cover problem in computational complexity theory is the algorithmic problem of finding a minimum clique cover, or (rephrased as a decision problem) finding a clique cover whose number of cliques is below a given threshold. Finding a minimum clique cover is NP-hard, and its decision version is NP-complete.
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