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The party problem, also known as the maximum clique problem, asks to find the minimum number of guests that must be invited so that at least m will know each other or at ...

An encoding which provides a bijection between the n^(n-2) labeled trees on n nodes and strings of n-2 integers chosen from an alphabet of the numbers 1 to n. A labeled tree ...

Let a random n×n (0,1)-matrix have entries which are 1 (with probability p) or 0 (with probability q=1-p) and numbers are assigned to the edges of a grid. A b-cluster is an ...

The beta function B(p,q) is the name used by Legendre and Whittaker and Watson (1990) for the beta integral (also called the Eulerian integral of the first kind). It is ...

P(n), sometimes also denoted p(n) (Abramowitz and Stegun 1972, p. 825; Comtet 1974, p. 94; Hardy and Wright 1979, p. 273; Conway and Guy 1996, p. 94; Andrews 1998, p. 1), ...

Connectivity properties obey the following hierarchy: convex => star convex => pathwise-connected => connected.

A binary relation associated with an instance of the stable marriage problem. Stable marriages correspond to vertices with outdegree 0 in the divorce digraph (Skiena 1990, p. ...

A binary tree in which special nodes are added wherever a null subtree was present in the original tree so that each node in the original tree (except the root node) has ...

A limb of a tree at a vertex v is the union of one or more branches at v in the tree. v is then called the base of the limb.

It is conjectured that every tree with e edges whose nodes are all trivalent or monovalent can be given a "magic" labeling such that the integers 1, 2, ..., e can be assigned ...