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The network flow problem considers a graph G with a set of sources S and sinks T and for which each edge has an assigned capacity (weight), and then asks to find the maximum ...

Tutte (1971/72) conjectured that there are no 3-connected nonhamiltonian bicubic graphs. However, a counterexample was found by J. D. Horton in 1976 (Gropp 1990), and several ...

The traveling salesman problem is a problem in graph theory requiring the most efficient (i.e., least total distance) Hamiltonian cycle a salesman can take through each of n ...

Let C be a curve, let O be a fixed point (the pole), and let O^' be a second fixed point. Let P and P^' be points on a line through O meeting C at Q such that P^'Q=QP=QO^'. ...

Two lattice points (x,y) and (x^',y^') are mutually visible if the line segment joining them contains no further lattice points. This corresponds to the requirement that ...

A cycle of a finite group G is a minimal set of elements {A^0,A^1,...,A^n} such that A^0=A^n=I, where I is the identity element. A diagram of a group showing every cycle in ...

The Hadwiger-Nelson problem asks for the chromatic number of the plane, i.e., the minimum number of colors needed to color the plane if no two points at unit distance one ...

The circumtangential triangle is an equilateral triangle formed by the three points X on the circumcircle of a reference triangle DeltaABC at which the line XX^(-1), where ...

A curve whose name means "shell form." Let C be a curve and O a fixed point. Let P and P^' be points on a line from O to C meeting it at Q, where P^'Q=QP=k, with k a given ...

A number which can be represented by a finite number of additions, subtractions, multiplications, divisions, and finite square root extractions of integers. Such numbers ...