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This PR introduces a basic s–t flow setup for undirected SimpleGraphs and proves the standard weak-duality
inequality: for any feasible flow f and any s–t cut S, value f ≤ cutCapacity S.

This is a small, self-contained lemma I extracted while working on larger graph-theoretic formalizations, in particular, results that will ultimately rely on a full max-flow/min-cut theorem. The full MFMC equality/existence statement is not included here. This is the weak-duality direction (∀ f S, value f ≤ cutCapacity S).

@github-actions github-actions bot added new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! t-combinatorics Combinatorics labels Jan 16, 2026
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PR summary 3de2350c1f

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.Combinatorics.SimpleGraph.Connectivity.MaxFlowMinCut (new file) 587

Declarations diff

+ Flow
+ cutCapacity
+ cutValue
+ cutValue_le_cutCapacity
+ netOut
+ netOut_def
+ value
+ value_def
+ value_eq_cutValue
+ value_le_cutCapacity

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.


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).

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github-actions bot commented Jan 16, 2026

✅ PR Title Formatted Correctly

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

@floor-licker floor-licker changed the title feat(SimpleGraph): add max-flow/min-cut weak duality feat(SimpleGraph): add max-flow/min-cut weak duality Jan 16, 2026
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