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A field is any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra. An archaic name for a field is ...

A tree is a mathematical structure that can be viewed as either a graph or as a data structure. The two views are equivalent, since a tree data structure contains not only a ...

Let I(G) denote the set of all independent sets of vertices of a graph G, and let I(G,u) denote the independent sets of G that contain the vertex u. A fractional coloring of ...

The network flow problem considers a graph G with a set of sources S and sinks T and for which each edge has an assigned capacity (weight), and then asks to find the maximum ...

An alternating group is a group of even permutations on a set of length n, denoted A_n or Alt(n) (Scott 1987, p. 267). Alternating groups are therefore permutation groups. ...

A graph G=(V,E) is an interval graph if it captures the intersection relation for some set of intervals on the real line. Formally, P is an interval graph provided that one ...

Tarski's theorem says that the first-order theory of reals with +, *, =, and > allows quantifier elimination. Algorithmic quantifier elimination implies decidability assuming ...

If k|n, then the complete k-uniform hypergraph on n vertices decomposes into 1-factors, where a 1-factor is a set of n/k pairwise disjoint k-sets. Brouwer and Schrijver ...

Let V be a vector space over a field K, and let A be a nonempty set. Now define addition p+a in A for any vector a in V and element p in A subject to the conditions: 1. ...

The (n,k)-arrangement graph A_(n,k) is defined as the graph on the vertex set consisting of the permutations of {1,2,...,n} containing at most k elements where vertices are ...