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A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres ...

An automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is ...

A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i.e., closed loop) through a graph that visits each node ...

A prime gap of length n is a run of n-1 consecutive composite numbers between two successive primes. Therefore, the difference between two successive primes p_k and p_(k+1) ...

Let Sigma(n)=sum_(i=1)^np_i (1) be the sum of the first n primes (i.e., the sum analog of the primorial function). The first few terms are 2, 5, 10, 17, 28, 41, 58, 77, ... ...

A graph is said to be regular of degree r if all local degrees are the same number r. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, ...

The Ackermann function is the simplest example of a well-defined total function which is computable but not primitive recursive, providing a counterexample to the belief in ...

The set R union {+infty,-infty} obtained by adjoining two improper elements to the set R of real numbers is normally called the set of (affinely) extended real numbers. ...

In a given circle, find an isosceles triangle whose legs pass through two given points inside the circle. This can be restated as: from two points in the plane of a circle, ...

Let s(n)=sigma(n)-n, where sigma(n) is the divisor function and s(n) is the restricted divisor function. Then the sequence of numbers s^0(n)=n,s^1(n)=s(n),s^2(n)=s(s(n)),... ...