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Let alpha(G) denote the independence number of a graph G. Then the Shannon capacity Theta(G), sometimes also denoted c(G), of G is defined as ...

A maximum clique of a graph G is a clique (i.e., complete subgraph) of maximum possible size for G. Note that some authors refer to maximum cliques simply as "cliques." The ...

Suppose a,b in N, n=ab+1, and x_1, ..., x_n is a sequence of n real numbers. Then this sequence contains a monotonic increasing (decreasing) subsequence of a+1 terms or a ...

The number q in a fraction p/q.

The number 13.

A friend of a number n is another number m such that (m,n) is a friendly pair.

A negative number multiplied by another negative number gives a positive number.

The blow-up lemma essentially says that regular pairs in Szemerédi's regularity lemma behave like complete bipartite graphs from the point of view of embedding bounded degree ...

A generalization of Turán's theorem to non-complete graphs.

A type of mathematical result which is considered by most logicians as more natural than the metamathematical incompleteness results first discovered by Gödel. Finite ...