[Merged by Bors] - feat(Combinatorics/SimpleGraph/Acyclic): every graph has a spanning forest

[thomaskwaring]

We show that every graph has a spanning forest: defined to be an acyclic subgraph with the same reachability relation as the larger graph. As a special case, every connected graph has a spanning tree.

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Each of these results (spanning forest & spanning tree) are proved in two versions: a general case where the forest / tree is found by extending a given acyclic subgraph, and the special case where that subgraph is empty.

• depends on: [Merged by Bors] - feat(Combinatorics/SimpleGraph/Acyclic): characterise maximal acyclic subgraphs #32043

[github-actions]

PR summary c3a9c0bd27

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ Connected.exists_isTree_le_of_le_of_isAcyclic
+ exists_isAcyclic_reachable_eq_le
+ exists_isAcyclic_reachable_eq_le_of_le_of_isAcyclic

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 scripts/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:

• [Merged by Bors] - feat(Combinatorics/SimpleGraph/Acyclic): characterise maximal acyclic subgraphs #32043
  By Dependent Issues (🤖). Happy coding!

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[b-mehta]

Very nice, thank you!

bors d+

[mathlib-bors]

✌️ thomaskwaring can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[thomaskwaring]

thanks!

bors r+

[mathlib-bors]

Pull request successfully merged into master.

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