combinatorics.simple_graph.matching
⟷
Mathlib.Combinatorics.SimpleGraph.Matching
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -124,7 +124,7 @@ theorem isMatching_iff_forall_degree {M : Subgraph G} [∀ v : V, Fintype (M.nei
theorem IsMatching.even_card {M : Subgraph G} [Fintype M.verts] (h : M.IsMatching) :
Even M.verts.toFinset.card := by
classical
- rw [is_matching_iff_forall_degree] at h
+ rw [is_matching_iff_forall_degree] at h
use M.coe.edge_finset.card
rw [← two_mul, ← M.coe.sum_degrees_eq_twice_card_edges]
simp [h, Finset.card_univ]
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -122,7 +122,12 @@ theorem isMatching_iff_forall_degree {M : Subgraph G} [∀ v : V, Fintype (M.nei
#print SimpleGraph.Subgraph.IsMatching.even_card /-
theorem IsMatching.even_card {M : Subgraph G} [Fintype M.verts] (h : M.IsMatching) :
- Even M.verts.toFinset.card := by classical
+ Even M.verts.toFinset.card := by
+ classical
+ rw [is_matching_iff_forall_degree] at h
+ use M.coe.edge_finset.card
+ rw [← two_mul, ← M.coe.sum_degrees_eq_twice_card_edges]
+ simp [h, Finset.card_univ]
#align simple_graph.subgraph.is_matching.even_card SimpleGraph.Subgraph.IsMatching.even_card
-/
@@ -146,7 +151,7 @@ theorem isPerfectMatching_iff_forall_degree {M : Subgraph G} [∀ v, Fintype (M.
#print SimpleGraph.Subgraph.IsPerfectMatching.even_card /-
theorem IsPerfectMatching.even_card {M : Subgraph G} [Fintype V] (h : M.IsPerfectMatching) :
- Even (Fintype.card V) := by classical
+ Even (Fintype.card V) := by classical simpa [h.2.card_verts] using is_matching.even_card h.1
#align simple_graph.subgraph.is_perfect_matching.even_card SimpleGraph.Subgraph.IsPerfectMatching.even_card
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -122,12 +122,7 @@ theorem isMatching_iff_forall_degree {M : Subgraph G} [∀ v : V, Fintype (M.nei
#print SimpleGraph.Subgraph.IsMatching.even_card /-
theorem IsMatching.even_card {M : Subgraph G} [Fintype M.verts] (h : M.IsMatching) :
- Even M.verts.toFinset.card := by
- classical
- rw [is_matching_iff_forall_degree] at h
- use M.coe.edge_finset.card
- rw [← two_mul, ← M.coe.sum_degrees_eq_twice_card_edges]
- simp [h, Finset.card_univ]
+ Even M.verts.toFinset.card := by classical
#align simple_graph.subgraph.is_matching.even_card SimpleGraph.Subgraph.IsMatching.even_card
-/
@@ -151,7 +146,7 @@ theorem isPerfectMatching_iff_forall_degree {M : Subgraph G} [∀ v, Fintype (M.
#print SimpleGraph.Subgraph.IsPerfectMatching.even_card /-
theorem IsPerfectMatching.even_card {M : Subgraph G} [Fintype V] (h : M.IsPerfectMatching) :
- Even (Fintype.card V) := by classical simpa [h.2.card_verts] using is_matching.even_card h.1
+ Even (Fintype.card V) := by classical
#align simple_graph.subgraph.is_perfect_matching.even_card SimpleGraph.Subgraph.IsPerfectMatching.even_card
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2020 Alena Gusakov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alena Gusakov, Arthur Paulino, Kyle Miller
-/
-import Mathbin.Combinatorics.SimpleGraph.DegreeSum
-import Mathbin.Combinatorics.SimpleGraph.Subgraph
+import Combinatorics.SimpleGraph.DegreeSum
+import Combinatorics.SimpleGraph.Subgraph
#align_import combinatorics.simple_graph.matching from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2020 Alena Gusakov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alena Gusakov, Arthur Paulino, Kyle Miller
-
-! This file was ported from Lean 3 source module combinatorics.simple_graph.matching
-! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Combinatorics.SimpleGraph.DegreeSum
import Mathbin.Combinatorics.SimpleGraph.Subgraph
+#align_import combinatorics.simple_graph.matching from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
+
/-!
# Matchings
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -127,10 +127,10 @@ theorem isMatching_iff_forall_degree {M : Subgraph G} [∀ v : V, Fintype (M.nei
theorem IsMatching.even_card {M : Subgraph G} [Fintype M.verts] (h : M.IsMatching) :
Even M.verts.toFinset.card := by
classical
- rw [is_matching_iff_forall_degree] at h
- use M.coe.edge_finset.card
- rw [← two_mul, ← M.coe.sum_degrees_eq_twice_card_edges]
- simp [h, Finset.card_univ]
+ rw [is_matching_iff_forall_degree] at h
+ use M.coe.edge_finset.card
+ rw [← two_mul, ← M.coe.sum_degrees_eq_twice_card_edges]
+ simp [h, Finset.card_univ]
#align simple_graph.subgraph.is_matching.even_card SimpleGraph.Subgraph.IsMatching.even_card
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -127,7 +127,7 @@ theorem isMatching_iff_forall_degree {M : Subgraph G} [∀ v : V, Fintype (M.nei
theorem IsMatching.even_card {M : Subgraph G} [Fintype M.verts] (h : M.IsMatching) :
Even M.verts.toFinset.card := by
classical
- rw [is_matching_iff_forall_degree] at h
+ rw [is_matching_iff_forall_degree] at h
use M.coe.edge_finset.card
rw [← two_mul, ← M.coe.sum_degrees_eq_twice_card_edges]
simp [h, Finset.card_univ]
mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alena Gusakov, Arthur Paulino, Kyle Miller
! This file was ported from Lean 3 source module combinatorics.simple_graph.matching
-! leanprover-community/mathlib commit 138448ae98f529ef34eeb61114191975ee2ca508
+! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.Combinatorics.SimpleGraph.Subgraph
/-!
# Matchings
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
A *matching* for a simple graph is a set of disjoint pairs of adjacent vertices, and the set of all
the vertices in a matching is called its *support* (and sometimes the vertices in the support are
said to be *saturated* by the matching). A *perfect matching* is a matching whose support contains
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1
@@ -51,6 +51,7 @@ variable {V : Type u} {G : SimpleGraph V} (M : Subgraph G)
namespace Subgraph
+#print SimpleGraph.Subgraph.IsMatching /-
/--
The subgraph `M` of `G` is a matching if every vertex of `M` is incident to exactly one edge in `M`.
We say that the vertices in `M.support` are *matched* or *saturated*.
@@ -58,13 +59,17 @@ We say that the vertices in `M.support` are *matched* or *saturated*.
def IsMatching : Prop :=
∀ ⦃v⦄, v ∈ M.verts → ∃! w, M.Adj v w
#align simple_graph.subgraph.is_matching SimpleGraph.Subgraph.IsMatching
+-/
+#print SimpleGraph.Subgraph.IsMatching.toEdge /-
/-- Given a vertex, returns the unique edge of the matching it is incident to. -/
noncomputable def IsMatching.toEdge {M : Subgraph G} (h : M.IsMatching) (v : M.verts) :
M.edgeSetEmbedding :=
⟨⟦(v, (h v.property).some)⟧, (h v.property).choose_spec.1⟩
#align simple_graph.subgraph.is_matching.to_edge SimpleGraph.Subgraph.IsMatching.toEdge
+-/
+#print SimpleGraph.Subgraph.IsMatching.toEdge_eq_of_adj /-
theorem IsMatching.toEdge_eq_of_adj {M : Subgraph G} (h : M.IsMatching) {v w : V} (hv : v ∈ M.verts)
(hvw : M.Adj v w) : h.toEdge ⟨v, hv⟩ = ⟨⟦(v, w)⟧, hvw⟩ :=
by
@@ -72,38 +77,50 @@ theorem IsMatching.toEdge_eq_of_adj {M : Subgraph G} (h : M.IsMatching) {v w : V
congr
exact ((h (M.edge_vert hvw)).choose_spec.2 w hvw).symm
#align simple_graph.subgraph.is_matching.to_edge_eq_of_adj SimpleGraph.Subgraph.IsMatching.toEdge_eq_of_adj
+-/
+#print SimpleGraph.Subgraph.IsMatching.toEdge.surjective /-
theorem IsMatching.toEdge.surjective {M : Subgraph G} (h : M.IsMatching) :
Function.Surjective h.toEdge := by
rintro ⟨e, he⟩
refine' Sym2.ind (fun x y he => _) e he
exact ⟨⟨x, M.edge_vert he⟩, h.to_edge_eq_of_adj _ he⟩
#align simple_graph.subgraph.is_matching.to_edge.surjective SimpleGraph.Subgraph.IsMatching.toEdge.surjective
+-/
+#print SimpleGraph.Subgraph.IsMatching.toEdge_eq_toEdge_of_adj /-
theorem IsMatching.toEdge_eq_toEdge_of_adj {M : Subgraph G} {v w : V} (h : M.IsMatching)
(hv : v ∈ M.verts) (hw : w ∈ M.verts) (ha : M.Adj v w) : h.toEdge ⟨v, hv⟩ = h.toEdge ⟨w, hw⟩ :=
by
rw [h.to_edge_eq_of_adj hv ha, h.to_edge_eq_of_adj hw (M.symm ha), Subtype.mk_eq_mk, Sym2.eq_swap]
#align simple_graph.subgraph.is_matching.to_edge_eq_to_edge_of_adj SimpleGraph.Subgraph.IsMatching.toEdge_eq_toEdge_of_adj
+-/
+#print SimpleGraph.Subgraph.IsPerfectMatching /-
/-- The subgraph `M` of `G` is a perfect matching on `G` if it's a matching and every vertex `G` is
matched.
-/
def IsPerfectMatching : Prop :=
M.IsMatching ∧ M.IsSpanning
#align simple_graph.subgraph.is_perfect_matching SimpleGraph.Subgraph.IsPerfectMatching
+-/
+#print SimpleGraph.Subgraph.IsMatching.support_eq_verts /-
theorem IsMatching.support_eq_verts {M : Subgraph G} (h : M.IsMatching) : M.support = M.verts :=
by
refine' M.support_subset_verts.antisymm fun v hv => _
obtain ⟨w, hvw, -⟩ := h hv
exact ⟨_, hvw⟩
#align simple_graph.subgraph.is_matching.support_eq_verts SimpleGraph.Subgraph.IsMatching.support_eq_verts
+-/
+#print SimpleGraph.Subgraph.isMatching_iff_forall_degree /-
theorem isMatching_iff_forall_degree {M : Subgraph G} [∀ v : V, Fintype (M.neighborSet v)] :
M.IsMatching ↔ ∀ v : V, v ∈ M.verts → M.degree v = 1 := by simpa [degree_eq_one_iff_unique_adj]
#align simple_graph.subgraph.is_matching_iff_forall_degree SimpleGraph.Subgraph.isMatching_iff_forall_degree
+-/
+#print SimpleGraph.Subgraph.IsMatching.even_card /-
theorem IsMatching.even_card {M : Subgraph G} [Fintype M.verts] (h : M.IsMatching) :
Even M.verts.toFinset.card := by
classical
@@ -112,7 +129,9 @@ theorem IsMatching.even_card {M : Subgraph G} [Fintype M.verts] (h : M.IsMatchin
rw [← two_mul, ← M.coe.sum_degrees_eq_twice_card_edges]
simp [h, Finset.card_univ]
#align simple_graph.subgraph.is_matching.even_card SimpleGraph.Subgraph.IsMatching.even_card
+-/
+#print SimpleGraph.Subgraph.isPerfectMatching_iff /-
theorem isPerfectMatching_iff : M.IsPerfectMatching ↔ ∀ v, ∃! w, M.Adj v w :=
by
refine' ⟨_, fun hm => ⟨fun v hv => hm v, fun v => _⟩⟩
@@ -121,15 +140,20 @@ theorem isPerfectMatching_iff : M.IsPerfectMatching ↔ ∀ v, ∃! w, M.Adj v w
· obtain ⟨w, hw, -⟩ := hm v
exact M.edge_vert hw
#align simple_graph.subgraph.is_perfect_matching_iff SimpleGraph.Subgraph.isPerfectMatching_iff
+-/
+#print SimpleGraph.Subgraph.isPerfectMatching_iff_forall_degree /-
theorem isPerfectMatching_iff_forall_degree {M : Subgraph G} [∀ v, Fintype (M.neighborSet v)] :
M.IsPerfectMatching ↔ ∀ v, M.degree v = 1 := by
simp [degree_eq_one_iff_unique_adj, is_perfect_matching_iff]
#align simple_graph.subgraph.is_perfect_matching_iff_forall_degree SimpleGraph.Subgraph.isPerfectMatching_iff_forall_degree
+-/
+#print SimpleGraph.Subgraph.IsPerfectMatching.even_card /-
theorem IsPerfectMatching.even_card {M : Subgraph G} [Fintype V] (h : M.IsPerfectMatching) :
Even (Fintype.card V) := by classical simpa [h.2.card_verts] using is_matching.even_card h.1
#align simple_graph.subgraph.is_perfect_matching.even_card SimpleGraph.Subgraph.IsPerfectMatching.even_card
+-/
end Subgraph
mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49
@@ -60,7 +60,8 @@ def IsMatching : Prop :=
#align simple_graph.subgraph.is_matching SimpleGraph.Subgraph.IsMatching
/-- Given a vertex, returns the unique edge of the matching it is incident to. -/
-noncomputable def IsMatching.toEdge {M : Subgraph G} (h : M.IsMatching) (v : M.verts) : M.edgeSet :=
+noncomputable def IsMatching.toEdge {M : Subgraph G} (h : M.IsMatching) (v : M.verts) :
+ M.edgeSetEmbedding :=
⟨⟦(v, (h v.property).some)⟧, (h v.property).choose_spec.1⟩
#align simple_graph.subgraph.is_matching.to_edge SimpleGraph.Subgraph.IsMatching.toEdge
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Sym2
's global Prod
setoid instance, use s(x, y)
notation for unordered pairs (#8729)
The Sym2
type used a global setoid instance on α × α
so that ⟦(x, y)⟧
could stand for an unordered pair using standard Quotient
syntax. This commit refactors Sym2
to not use Quotient
and instead use its own s(x, y)
notation. One benefit to this is that this notation produces a term with type Sym2
rather than Quotient
.
The Fintype
instance for Sym2
is in Mathlib.Data.Finset.Sym
. We switch from using the one for Quotient
because it does not require DecidableEq
.
@@ -57,11 +57,11 @@ def IsMatching : Prop := ∀ ⦃v⦄, v ∈ M.verts → ∃! w, M.Adj v w
/-- Given a vertex, returns the unique edge of the matching it is incident to. -/
noncomputable def IsMatching.toEdge {M : Subgraph G} (h : M.IsMatching) (v : M.verts) : M.edgeSet :=
- ⟨⟦(v, (h v.property).choose)⟧, (h v.property).choose_spec.1⟩
+ ⟨s(v, (h v.property).choose), (h v.property).choose_spec.1⟩
#align simple_graph.subgraph.is_matching.to_edge SimpleGraph.Subgraph.IsMatching.toEdge
theorem IsMatching.toEdge_eq_of_adj {M : Subgraph G} (h : M.IsMatching) {v w : V} (hv : v ∈ M.verts)
- (hvw : M.Adj v w) : h.toEdge ⟨v, hv⟩ = ⟨⟦(v, w)⟧, hvw⟩ := by
+ (hvw : M.Adj v w) : h.toEdge ⟨v, hv⟩ = ⟨s(v, w), hvw⟩ := by
simp only [IsMatching.toEdge, Subtype.mk_eq_mk]
congr
exact ((h (M.edge_vert hvw)).choose_spec.2 w hvw).symm
@@ -2,15 +2,12 @@
Copyright (c) 2020 Alena Gusakov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alena Gusakov, Arthur Paulino, Kyle Miller
-
-! This file was ported from Lean 3 source module combinatorics.simple_graph.matching
-! leanprover-community/mathlib commit 138448ae98f529ef34eeb61114191975ee2ca508
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Combinatorics.SimpleGraph.DegreeSum
import Mathlib.Combinatorics.SimpleGraph.Subgraph
+#align_import combinatorics.simple_graph.matching from "leanprover-community/mathlib"@"138448ae98f529ef34eeb61114191975ee2ca508"
+
/-!
# Matchings
The unported dependencies are