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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 .
A maximum clique transversal of a graph is a subset of vertices with the property that each maximum clique of the graph contains at least one vertex in the subset. [2] The opposite of a clique is an independent set, in the sense that every clique corresponds to an independent set in the complement graph.
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 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 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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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).
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