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H(3,3) drawn as a unit distance graph Hamming graphs are a special class of graphs named after Richard Hamming and used in several branches of mathematics ( graph theory ) and computer science . Let S be a set of q elements and d a positive integer .
The Hadwiger–Nelson problem concerns the chromatic number of unit distance graphs, and more specifically of the infinite unit distance graph formed from all points of the Euclidean plane. By the de Bruijn–Erdős theorem , which assumes the axiom of choice , this is equivalent to asking for the largest chromatic number of a finite unit ...
In geometric graph theory, the Hadwiger–Nelson problem, named after Hugo Hadwiger and Edward Nelson, asks for the minimum number of colors required to color the plane such that no two points at distance one from each other have the same color. The answer is unknown, but has been narrowed down to one of the numbers 4, 5, 6 or 7.
In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a metric or distance function. [1] Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
A Voronoi diagram is a special kind of decomposition of a metric space determined by distances to a specified discrete set of objects in the space, e.g., by a discrete set of points. This diagram is named after Georgy Voronoi , also called a Voronoi tessellation , a Voronoi decomposition, or a Dirichlet tessellation after Peter Gustav Lejeune ...