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A graph H is called a topological minor, also known as a homeomorphic subgraph, of a graph G if a graph subdivision of H is isomorphic to a subgraph of G. Every topological ...

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 ...

Percolation theory deals with fluid flow (or any other similar process) in random media. If the medium is a set of regular lattice points, then there are two main types of ...

An Eulerian path, also called an Euler chain, Euler trail, Euler walk, or "Eulerian" version of any of these variants, is a walk on the graph edges of a graph which uses each ...

A polyhedron or plane tessellation is called semiregular if its faces are all regular polygons and its corners are alike (Walsh 1972; Coxeter 1973, pp. 4 and 58; Holden 1991, ...

Let N^* be the smallest dimension n of a hypercube such that if the lines joining all pairs of corners are two-colored for any n>=N^*, a complete graph K_4 of one color with ...

A regular surface M subset R^n is called orientable if each tangent space M_p has a complex structure J_p:M_p->M_p such that p->J_p is a continuous function.

A right pyramid is a pyramid for which the apex lies directly above the centroid of the base. A regular pyramid is therefore a special case of a right pyramid.

z(1-z)(d^2y)/(dz^2)+[c-(a+b+1)z](dy)/(dz)-aby=0. It has regular singular points at 0, 1, and infty. Every second-order ordinary differential equation with at most three ...

The matrix tree theorem, also called Kirchhoff's matrix-tree theorem (Buekenhout and Parker 1998), states that the number of nonidentical spanning trees of a graph G is equal ...