Concrete colorings of common graphs #
This file defines colorings for some common graphs
Main declarations #
SimpleGraph.pathGraph.bicoloring
: Bicoloring of a path graph.
Bicoloring of a path graph
Equations
- SimpleGraph.pathGraph.bicoloring n = SimpleGraph.Coloring.mk (fun (u : Fin n) => decide (↑u % 2 = 0)) ⋯
Instances For
def
SimpleGraph.pathGraph_two_embedding
(n : ℕ)
(h : 2 ≤ n)
:
(SimpleGraph.pathGraph 2).Embedding (SimpleGraph.pathGraph n)
Embedding of pathGraph 2
into the first two elements of pathGraph n
for 2 ≤ n
Equations
- SimpleGraph.pathGraph_two_embedding n h = { toFun := fun (v : Fin 2) => ⟨↑v, ⋯⟩, inj' := ⋯, map_rel_iff' := ⋯ }
Instances For
theorem
SimpleGraph.chromaticNumber_pathGraph
(n : ℕ)
(h : 2 ≤ n)
:
(SimpleGraph.pathGraph n).chromaticNumber = 2