SizeRamsey.lean`

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Size Ramsey Number

This file defines the size Ramsey number for simple graphs.

Definition

The size Ramsey number r̂(G, H) is the minimum number of edges in a graph F such that any 2-coloring of F's edges contains a copy of G in one color or H in the other.

Imports (3)

Imported by 1 file

FormalConjecturesForMathlib.lean

def SimpleGraph.sizeRamsey The size Ramsey number r̂(G, H) is the minimum number of edges in a graph F such that any 2-coloring of F's edges contains a copy of G in one color or H in the other line 43 source
Source documentation
The size Ramsey number r̂(G, H) is the minimum number of edges in a graph F such that any 2-coloring of F's edges contains a copy of G in one color or H in the other.
A 2-coloring is represented by a subgraph R ≤ F (the "red" edges); the "blue" edges are F \ R.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Fintype, SimpleGraph, Nat
Proof uses: InfSet.sInf, Set.ofPred, Exists, Fin, And, Eq, Set.ncard, Sym2, SimpleGraph.edgeSet, LE.le, Or, SimpleGraph.IsContained, SDiff.sdiff
3 instances, coercions and auxiliary constants left out.
```
noncomputable def sizeRamsey {α β : Type*} [Fintype α] [Fintype β]
    (G : SimpleGraph α) (H : SimpleGraph β) : ℕ :=
…
```