Theorems · Definition · combinatorics
SimpleGraph.completeGraph
(V : Type u) → SimpleGraph V
The complete graph on a type V is the simple graph with all pairs of distinct vertices.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Basic
- Cited by
- 49 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.
Cites2
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
Cited by54
Results whose statement or proof uses this declaration.
- SimpleGraph.Coloringproof · cited by 44
- SimpleGraph.Coloring.validstatement · cited by 11
- SimpleGraph.Embedding.completeGraphstatement · cited by 9
- SimpleGraph.not_cliqueFree_iff_top_isContainedstatement · cited by 7
- SimpleGraph.Iso.completeGraphstatement · cited by 4
- SimpleGraph.cliqueFree_iffstatement · cited by 4
- SimpleGraph.IsContained.not_cliqueFreestatement and proof · cited by 3
- SimpleGraph.CliqueFree.replaceVertexproof · cited by 3
- SimpleGraph.comap_topstatement · cited by 2
- SimpleGraph.card_le_chromaticNumber_iff_forall_surjectivestatement · cited by 2
- SimpleGraph.compl_adjMatrix_completeGraphstatement · cited by 2
- SimpleGraph.IsBipartite.exists_isBipartiteWithproof · cited by 2