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Mycielski's Theorem

Combinatorics and Graph Theory

Mycielski's theorem, in graph theory, follows from the construction Jan Mycielski introduced in 1955, known as the Mycielskian, which builds a larger graph from a given one. Applying the construction preserves the property of being triangle-free while increasing the chromatic number, so repeatedly applying it to a triangle-free starting graph shows that triangle-free graphs can have arbitrarily large chromatic numbers, the result now known as Mycielski's theorem. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

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Existence Theorem 1
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Source Graph Coloring (Wikipedia)
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1. Mycielskian (Wikipedia)
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Quote, Lead section
In the mathematical area of graph theory, the Mycielskian or Mycielski graph of an undirected graph is a larger graph formed from it by a construction of Jan Mycielski (1955).
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Graph Coloring (Wikipedia)
Wikimedia FoundationIn Branch: Graph Theory, Lead sentence
Quote, In Branch: Graph Theory, Lead sentence
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph.
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