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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.
In graph theory, a branch of combinatorial mathematics, a block graph or clique tree [1] is a type of undirected graph in which every biconnected component (block) is a clique. Block graphs are sometimes erroneously called Husimi trees (after Kôdi Husimi ), [ 2 ] but that name more properly refers to cactus graphs , graphs in which every ...
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 number ω(G) is the number of vertices in a maximum clique of G. [1] Several closely related clique-finding problems have been studied. [14] In the maximum clique problem, the input is an undirected graph, and the output is a maximum clique in the graph. If there are multiple maximum cliques, one of them may be chosen arbitrarily. [14]
The clique complex can also be viewed as a topological space in which each clique of k vertices is represented by a simplex of dimension k – 1. The 1-skeleton of X ( G ) (also known as the underlying graph of the complex) is an undirected graph with a vertex for every 1-element set in the family and an edge for every 2-element set in the ...
The post 26 Palindrome Examples: Words and Phrases That Are the Same Backwards and Forwards appeared first on Reader's Digest. Palindrome words are spelled the same backward and forward.
The basic form of the Bron–Kerbosch algorithm is a recursive backtracking algorithm that searches for all maximal cliques in a given graph G.More generally, given three disjoint sets of vertices R, P, and X, it finds the maximal cliques that include all of the vertices in R, some of the vertices in P, and none of the vertices in X.
A clique cover of a graph G may be seen as a graph coloring of the complement graph of G, the graph on the same vertex set that has edges between non-adjacent vertices of G. Like clique covers, graph colorings are partitions of the set of vertices, but into subsets with no adjacencies (independent sets) rather than cliques.