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Mathlib.Combinatorics.SimpleGraph.ConcreteColorings

Concrete colorings of common graphs #

This file defines colorings for some common graphs

Main declarations #

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def SimpleGraph.pathGraph.bicoloring (n : ℕ) :
SimpleGraph.Coloring (SimpleGraph.pathGraph n) Bool

Bicoloring of a path graph

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    def SimpleGraph.pathGraph_two_embedding (n : ℕ) (h : 2 ≤ n) :
    SimpleGraph.pathGraph 2 ↪g SimpleGraph.pathGraph n

    Embedding of pathGraph 2 into the first two elements of pathGraph n for 2 ≤ n

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      theorem SimpleGraph.chromaticNumber_pathGraph (n : ℕ) (h : 2 ≤ n) :
      SimpleGraph.chromaticNumber (SimpleGraph.pathGraph n) = 2