…graph#825)

I think the auxiliary space and time complexity as recently updated in
petgraph#815, are not quite right for Bron-Kerbosch.

For one, the auxiliary space complexity cannot be right. Since, we
return a `Vec` with `HashSet`, the auxiliary space has to be at least
equal to the number of maximal cliques in the graph. [Moon and Moser
showed](https://link.springer.com/article/10.1007/BF02760024) that this
can be up to `3 ^ (|V| / 3)` many. Thus, I suggest introducing `k` as a
variable to denote the number of maximal cliques in the graph.

The time complexity might also be able to be written in terms of `k`,
however this would probably also depend on this implementation of
Bron-Kerbosch with pivoting. Instead one could write something like:

```
/// * Time complexity: **O(p(|V|)k)**
```
For some polynomial `p`, which makes clear that the runtime is not
always exponential in the number of vertices, but is merely dominated by
the number of maximal cliques in the graph.

## 🤖 New release

* `petgraph`: 0.8.2 -> 0.8.3 (✓ API compatible changes)

<details><summary><i><b>Changelog</b></i></summary><p>

<blockquote>

##
[0.8.3](https://github.com/petgraph/petgraph/compare/petgraph@v0.8.2...petgraph@v0.8.3)
- 2025-09-28

### Bug Fixes

- Infinite `subgraph_isomorphisms_iter` for empty isomorphisms
([#780](#780))
- Algos don't work on `UndirectedAdaptor`
([#870](#870))
([#871](#871))
- use a queue for SPFA
([#893](#893))
- `StableGraph::reverse` breaks free lists
([#890](#890))

### Documentation

- Fix examples link in README and unify typesetting of one word
([#823](#823))
- Add link to multigraph definition to isomorphism algos
([#824](#824))
- Fix auxiliary space (and time) complexity of bron-kerbosch
([#825](#825))
- Fix Typo in Operator Module Documentation
([#831](#831))
- Sync the crate feature flags in the README and docs
([#832](#832))
- Remove all \[Generic\] tags from algo docstrings
([#835](#835))
- Fix typos in comments
([#836](#836))
- Revamp CONTRIBUTING.md
([#833](#833))
- Update `GraphMap` link in README
([#857](#857))
- Add doc comment for `Dot::with_attr_getters`
([#850](#850))
- Specify iteration order for neighbors and edges and their variants
([#790](#790))
- Collection of Doc fixes
([#856](#856))

### New Features

- Add `into_nodes_edges_iters` to `StableGraph`
([#841](#841))
- Add methods to reserve & shrink `StableGraph` capacity
([#846](#846))
- Add Dinic's Maximum Flow Algorithm
([#739](#739))
- make Csr::from_sorted_edges generic over edge type and properly
increase edge_count in Csr::from_sorted_edges
([#861](#861))
- Add `map_owned` and `filter_map_owned` for `Graph` and `StableGraph`
([#863](#863))
- Add dijkstra::with_dynamic_goal
([#855](#855))
- Fix self-loop bug in all_simple_paths and enable multiple targets
([#865](#865))
- mark petgraph::dot::Dot::graph_fmt as public
([#866](#866))
- Add bidirectional Dijkstra algorithm
([#782](#782))

### Performance

- Make A* tie break on lower h-values
([#882](#882))

### Refactor

- add examples for scc algorithms and reorganize into dedicated module
([#830](#830))
- Remove unnecessary trait bounds from impls/methods
([#828](#828))
- replace uses of 'crate::util::zip' with 'core::iter::zip'
([#849](#849))
- Fix clippy (and other) lints
([#851](#851))
- Cleanup repo ([#854](#854))
- replace crate::util::enumerate with Iterator::enumerate
([#881](#881))

### Testing

- Add dependency list for 'quickcheck' feature
([#822](#822))
- Fix feature cfg capitalization in doctest
([#852](#852))
</blockquote>


</p></details>

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Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
Co-authored-by: Egor Starovoitov <52821033+starovoid@users.noreply.github.com>