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- Hadwiger–Nelson_problem abstract "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 1 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. The correct value may actually depend on the choice of axioms for set theory.The question can be phrased in graph theoretic terms as follows. Let G be the unit distance graph of the plane: an infinite graph with all points of the plane as vertices and with an edge between two vertices if and only if there is unit distance between the two points. Then the Hadwiger–Nelson problem is to find the chromatic number of G. As a consequence, the problem is often called "finding the chromatic number of the plane". By the de Bruijn–Erdős theorem, a result of de Bruijn & Erdős (1951), the problem is equivalent (under the assumption of the axiom of choice) to that of finding the largest possible chromatic number of a finite unit distance graph.According to Jensen & Toft (1995), the problem was first formulated by E. Nelson in 1950, and first published by Gardner (1960). Hadwiger (1945) published a related result, showing that any cover of the plane by five congruent closed sets contains a unit distance in one of the sets, and he also mentioned the problem in a later paper (Hadwiger 1961). Soifer (2008) discusses the problem and its history extensively.".
- Hadwiger–Nelson_problem thumbnail Hadwiger-Nelson.svg?width=300.
- Hadwiger–Nelson_problem wikiPageID "3133115".
- Hadwiger–Nelson_problem wikiPageRevisionID "551287741".
- Hadwiger–Nelson_problem subject Category:Geometric_graph_theory.
- Hadwiger–Nelson_problem subject Category:Graph_coloring.
- Hadwiger–Nelson_problem subject Category:Infinite_graphs.
- Hadwiger–Nelson_problem subject Category:Mathematical_problems.
- Hadwiger–Nelson_problem subject Category:Unsolved_problems_in_mathematics.
- Hadwiger–Nelson_problem comment "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 1 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. The correct value may actually depend on the choice of axioms for set theory.The question can be phrased in graph theoretic terms as follows.".
- Hadwiger–Nelson_problem label "Hadwiger–Nelson problem".
- Hadwiger–Nelson_problem label "Hadwiger–Nelson-Problem".
- Hadwiger–Nelson_problem label "Проблема Нелсона — Эрдёша — Хадвигера".
- Hadwiger–Nelson_problem label "哈德維格-納爾遜問題".
- Hadwiger–Nelson_problem sameAs Hadwiger%E2%80%93Nelson_problem.
- Hadwiger–Nelson_problem sameAs Hadwiger–Nelson-Problem.
- Hadwiger–Nelson_problem sameAs Q1383936.
- Hadwiger–Nelson_problem sameAs Q1383936.
- Hadwiger–Nelson_problem wasDerivedFrom Hadwiger–Nelson_problem?oldid=551287741.
- Hadwiger–Nelson_problem depiction Hadwiger-Nelson.svg.
