Theorems · Theorem · combinatorics
SimpleGraph.isBipartiteWith_sum_degrees_eq
∀ {V : Type u_1} {G : SimpleGraph V} {s t : Finset V} [inst : G.LocallyFinite],
G.IsBipartiteWith ↑s ↑t → ∑ v ∈ s, G.degree v = ∑ w ∈ t, G.degree wIf G.IsBipartiteWith s t, then the sum of the degrees of vertices in s is equal to the sum
of the degrees of vertices in t.
See Finset.sum_card_bipartiteAbove_eq_sum_card_bipartiteBelow.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SimpleGraph.LocallyFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidproof · cited by 12,281
- SetLike.coestatement and proof · cited by 8,199
- Finset.sumstatement and proof · cited by 5,195
- SimpleGraphstatement and proof · cited by 3,072
- Finset.cardproof · cited by 2,327
- SimpleGraph.Adjproof · cited by 1,346
- Subtype.propproof · cited by 505
- Finset.attachproof · cited by 168
- SimpleGraph.degreestatement and proof · cited by 112
- SimpleGraph.neighborFinsetproof · cited by 72
- Finset.sum_attachproof · cited by 54
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.isBipartiteWith_sum_degrees_eq_card_edgesproof · cited by 1