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A graph is a forbidden subgraph if its presence as a subgraph of a given graph means it is not a member of some family of graphs. For example, a bipartite graph is a graph ...

A graph is a forbidden topological minor (also known as a forbidden homeomorphic subgraph) if its presence as a homeomorphic subgraph of a given graph (i.e., there is an ...

A technique in set theory invented by P. Cohen (1963, 1964, 1966) and used to prove that the axiom of choice and continuum hypothesis are independent of one another in ...

Given an infinitive sequence {x_n} with associative array a(i,j), then {x_n} is said to be a fractal sequence 1. If i+1=x_n, then there exists m<n such that i=x_m, 2. If h<i, ...

Fubini's theorem, sometimes called Tonelli's theorem, establishes a connection between a multiple integral and a repeated one. If f(x,y) is continuous on the rectangular ...

Every polynomial equation having complex coefficients and degree >=1 has at least one complex root. This theorem was first proven by Gauss. It is equivalent to the statement ...

If two single-valued continuous functions kappa(s) (curvature) and tau(s) (torsion) are given for s>0, then there exists exactly one space curve, determined except for ...

An irrational number x can be called GK-regular (defined here for the first time) if the distribution of its continued fraction coefficients is the Gauss-Kuzmin distribution. ...

For a general two-player zero-sum game, max_(i<=m)min_(j<=n)a_(ij)<=min_(j<=n)max_(i<=m)a_(ij). If the two are equal, then write ...

A algebraic loop L is a generalized Bol loop if for all elements x, y, and z of L, ((xy)z)alpha(y)=x((yz)alpha(y)) for some map alpha:L->L. As the name suggests, these are ...