feat(Combinatorics/SimpleGraph): API for bipartite simple graph double-counting

[mitchell-horner]

Implement an API for bipartite double-counting arguments using simple graph definitions. Notably define the predicate IsBipartite: G.IsBipartite s t is the proposition that G is bipartite in sets s, t.

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• depends on: feat(Combinatorics/SimpleGraph): prove finite results for induced subgraphs of G.support #20825

[github-actions]

PR summary 7ef28bbfbb

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Combinatorics.SimpleGraph.Finite	559	563	+4 (+0.72%)

Import changes for all files

Files	Import difference
Mathlib.Combinatorics.SimpleGraph.DegreeSum	2
Mathlib.Combinatorics.SimpleGraph.IncMatrix	3
Mathlib.Combinatorics.SimpleGraph.Finite	4
Mathlib.Combinatorics.SimpleGraph.Bipartite (new file)	931

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Declarations diff

+ IsBipartite
+ IsBipartite.mem_of_mem_adj
+ IsBipartite.mem_of_mem_adj'
+ IsBipartite.symm
+ card_edgeFinset_induce_of_support_subset
+ card_edgeFinset_induce_support
+ card_support_le
+ degree_eq_zero_iff_not_mem_support
+ degree_induce_of_support_subset
+ degree_induce_support
+ instance : DecidablePred (· ∈ G.support) := by
+ isBipartite_bipartiteAbove
+ isBipartite_bipartiteBelow
+ isBipartite_comm
+ isBipartite_degree_le
+ isBipartite_degree_le'
+ isBipartite_neighborFinset
+ isBipartite_neighborFinset'
+ isBipartite_neighborFinset_disjoint
+ isBipartite_neighborFinset_disjoint'
+ isBipartite_neighborFinset_subset
+ isBipartite_neighborFinset_subset'
+ isBipartite_neighborSet
+ isBipartite_neighborSet'
+ isBipartite_neighborSet_disjoint
+ isBipartite_neighborSet_disjoint'
+ isBipartite_neighborSet_subset
+ isBipartite_neighborSet_subset'
+ isBipartite_sum_degrees_eq
+ isBipartite_sum_degrees_eq_card_edges
+ isBipartite_sum_degrees_eq_card_edges'
+ isBipartite_sum_degrees_eq_twice_card_edges
+ isBipartite_support_subset
+ sum_degrees_support_eq_twice_card_edges

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• feat(Combinatorics/SimpleGraph): prove finite results for induced subgraphs of G.support #20825
  By Dependent Issues (🤖). Happy coding!

[b-mehta]

It looks like there's quite a bit of overlap between this and the material in DoubleCounting.lean