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An edge coloring of a graph G is a coloring of the edges of G such that adjacent edges (or the edges bounding different regions) receive different colors. An edge coloring ...

A minimum edge cut of a graph is an edge cut of smallest possible size. The size of a minimum edge cut in a connected graph G is called the graph's edge connectivity ...

A minimum vertex cut of a graph is a vertex cut of smallest possible size. A vertex cut set of size 1 in a connected graph corresponds to an articulation vertex. The size of ...

Model theory is a general theory of interpretations of axiomatic set theory. It is the branch of logic studying mathematical structures by considering first-order sentences ...

The multinomial coefficients (n_1,n_2,...,n_k)!=((n_1+n_2+...+n_k)!)/(n_1!n_2!...n_k!) (1) are the terms in the multinomial series expansion. In other words, the number of ...

"Neighborhood" is a word with many different levels of meaning in mathematics. One of the most general concepts of a neighborhood of a point x in R^n (also called an ...

Let pi_n(x)=product_(k=0)^n(x-x_k), (1) then f(x)=f_0+sum_(k=1)^npi_(k-1)(x)[x_0,x_1,...,x_k]+R_n, (2) where [x_1,...] is a divided difference, and the remainder is ...

A proof which indirectly shows a mathematical object exists without providing a specific example or algorithm for producing an example. Nonconstructive proofs are also called ...

The word "normal form" is used in a variety of different ways in mathematics. In general, it refers to a way of representing objects so that, although each may have many ...

A set X is said to be nowhere dense if the interior of the set closure of X is the empty set. For example, the Cantor set is nowhere dense. There exist nowhere dense sets of ...