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Call a graph vertex m(a,b,c) a median of a graph G if it lies on all shortest paths between each pair of vertices (a,b), (b,a), and (c,a) in G. A median graph is then defined ...

A modification of Legendre's formula for the prime counting function pi(x). It starts with |_x_| = (1) where |_x_| is the floor function, P_2(x,a) is the number of integers ...

Let G be a graph with A and B two disjoint n-tuples of graph vertices. Then either G contains n pairwise disjoint AB-paths, each connecting a point of A and a point of B, or ...

A metric space is a set S with a global distance function (the metric g) that, for every two points x,y in S, gives the distance between them as a nonnegative real number ...

The midcircle of two given circles is the circle which would invert the circles into each other. Dixon (1991) gives constructions for the midcircle for four of the five ...

The radius rho of the midsphere of a polyhedron, also called the interradius. Let P be a point on the original polyhedron and P^' the corresponding point P on the dual. Then ...

det(i+j+mu; 2i-j)_(i,j=0)^(n-1)=2^(-n)product_(k=0)^(n-1)Delta_(2k)(2mu), where mu is an indeterminate, Delta_0(mu)=2, ...

Mills' constant can be defined as the least theta such that f_n=|_theta^(3^n)_| is prime for all positive integers n (Caldwell and Cheng 2005). The first few f_n for n=1, 2, ...

A Banach space X is called minimal if every infinite-dimensional subspace Y of X contains a subspace Z isomorphic to X. An example of a minimal Banach space is the Banach ...

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 ...