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Cliques in random graphs. (English) Zbl 0344.05155
The paper concerns random graphs. A random graph is defined here as a graph whose vertex set is the set of all positive integers and in which each edge occurs with the probability $$p$$ (this probability is the same for all pairs of vertices). A random variable $$X_n$$ is defined as the maximal size of a clique in such a random graph; various results concerning $$X_n$$ are proved. Further the existence of infinite cliques in a random graph and the number of colours necessary for colouring a random graph by means of the so-called greedy algorithm are investigated. A remark on hypergraphs is added.