Theorems · Definition · combinatorics
SimpleGraph.completeMultipartiteGraph
{ι : Type u_5} → (V : ι → Type u_6) → SimpleGraph ((i : ι) × V i)Given a family of vertex types indexed by ι, pulling back from ⊤ : SimpleGraph ι
yields the complete multipartite graph on the family.
Two vertices are adjacent if and only if their indices are not equal.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Maps
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- SimpleGraphstatement · cited by 3,072
- SimpleGraph.comapproof · cited by 29
Cited by15
Results whose statement or proof uses this declaration.
- SimpleGraph.completeMultipartiteGraph.topEmbeddingstatement · cited by 4
- SimpleGraph.completeMultipartiteGraph.not_cliqueFree_of_le_cardstatement and proof · cited by 3
- SimpleGraph.IsCompleteMultipartite.isostatement · cited by 2
- SimpleGraph.completeMultipartiteGraph.coloringstatement · cited by 2
- SimpleGraph.completeMultipartiteGraph.not_cliqueFree_of_infinitestatement · cited by 2
- SimpleGraph.completeEquipartiteGraph.completeMultipartiteGraphstatement · cited by 1
- SimpleGraph.completeMultipartiteGraph.colorablestatement · cited by 1
- SimpleGraph.completeMultipartiteGraph.colorable_of_cliqueFreestatement and proof · cited by 1
- SimpleGraph.isCompleteMultipartite_iffstatement and proof · cited by 1
- SimpleGraph.completeMultipartiteGraph.chromaticNumberstatement and proof · cited by 0
- SimpleGraph.completeMultipartiteGraph.isCompleteMultipartitestatement · cited by 0
- SimpleGraph.completeMultipartiteGraph.not_cliqueFree_of_le_enatCardstatement · cited by 0