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An independent edge set (also called a matching) of a graph G is a subset of the edges such that no two edges in the subset share a vertex of G (Skiena 1990, p. 219). The ...

Let (A,<=) and (B,<=) be disjoint totally ordered sets with order types alpha and beta. Then the ordinal sum is defined at set (C=A union B,<=) where, if c_1 and c_2 are both ...

In n-dimensional Lorentzian space R^n=R^(1,n-1), the light cone C^(n-1) is defined to be the subset consisting of all vectors x=(x_0,x_1,...,x_(n-1)) (1) whose squared ...

An amicable pair (m,n) consists of two integers m,n for which the sum of proper divisors (the divisors excluding the number itself) of one number equals the other. Amicable ...

Let G be a group, and let S subset= G be a set of group elements such that the identity element I not in S. The Cayley graph associated with (G,S) is then defined as the ...

An independent vertex set of a graph G is a subset of the vertices such that no two vertices in the subset represent an edge of G. Given a vertex cover of a graph, all ...

A Banach space X has the approximation property (AP) if, for every epsilon>0 and each compact subset K of X, there is a finite rank operator T in X such that for each x in K, ...

The closed graph theorem states that a linear operator between two Banach spaces X and Y is continuous iff it has a closed graph, where the "graph" {(x,f(x)):x in X} is ...

Let {f_n(x)} be a sequence of analytic functions regular in a region G, and let this sequence be uniformly convergent in every closed subset of G. If the analytic function ...

If a group of men and women may date only if they have previously been introduced, then a complete set of dates is possible iff every subset of men has collectively been ...