feat(SimpleGraph/Coloring/VertexColoring): Matching is 2 colorable

[robo7179]

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[github-actions]

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[github-actions]

PR summary 23ee525659

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

+ colorable_two_of_maxDegree_le_one

You can run this locally as follows

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

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

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

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No changes to technical debt.

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/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).

[github-actions]

✅ PR Title Formatted Correctly

The title of this PR has been updated to match our commit style conventions.
Thank you!

[SnirBroshi]

It's a general fact that a locally-finite graph is G.Colorable (G.maxDegree + 1), I don't think we should have a specific proof for 1.
I have the general proof, see colorable_maxDegree_add_one in #38357.
However a specific proof for Subgraph.Matching (as your title suggests) might be nice if it's simple.

[vlad902]

We don't seem to have (or I just missed) that matching subgraphs are bipartite. The result would then follow immediately.

EDIT: This is nonsense. SimpleGraph.IsBipartite is defined using 2-colorability so that makes no sense. I was originally thinking of the definition SimpleGraph.IsBipartiteWith though that's not really suitable here.

[mathlib-merge-conflicts]

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