Fix #47: Add HamiltonianCycle model

[GiggleLiu]

[action]

Summary

• Add HamiltonianCycle<G, W> optimization model: finds minimum-weight cycle visiting every vertex exactly once
• Edge-based binary variables (dims = [2; num_edges]), with validity check for degree-2, connectivity, and edge count
• Follows MaximumMatching pattern (edge weights, from_graph constructors, is_weighted())
• Includes paper documentation with problem-def and display-name entry

Closes #47

[codecov]

Codecov Report

❌ Patch coverage is 95.91837% with 12 lines in your changes missing coverage. Please review.
✅ Project coverage is 96.93%. Comparing base (d8eec69) to head (53c68d0).
⚠️ Report is 2 commits behind head on main.

Files with missing lines	Patch %	Lines
src/models/graph/traveling_salesman.rs	92.40%	12 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #57      +/-   ##
==========================================
- Coverage   96.94%   96.93%   -0.02%     
==========================================
  Files         174      176       +2     
  Lines       25043    25337     +294     
==========================================
+ Hits        24278    24560     +282     
- Misses        765      777      +12     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[Copilot]

Pull request overview

Adds a new graph optimization model, HamiltonianCycle<G, W>, to represent the minimum-weight Hamiltonian cycle problem, along with unit tests and documentation/schema registration so it appears in exported schemas and the paper.

Changes:

• Introduces HamiltonianCycle model (edge-based binary variables, validity check, objective evaluation, from_graph constructors) and exports it from graph/model modules and the crate prelude.
• Adds comprehensive unit tests exercising construction, validation, evaluation, and brute-force solving on small instances.
• Registers/updates documentation artifacts (problem schema JSON + paper display-name and problem-def) and adds an implementation plan document.

Reviewed changes

Copilot reviewed 8 out of 8 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
src/models/graph/hamiltonian_cycle.rs	New HamiltonianCycle model + schema registration + is_hamiltonian_cycle validator
src/models/graph/mod.rs	Wires new model into the graph module and re-exports it
src/models/mod.rs	Re-exports HamiltonianCycle at the models module level and updates category docs
src/lib.rs	Adds HamiltonianCycle to the crate prelude
src/unit_tests/models/graph/hamiltonian_cycle.rs	New unit tests for the model + brute-force solver behavior
docs/src/reductions/problem_schemas.json	Adds schema entry for HamiltonianCycle
docs/paper/reductions.typ	Adds paper display-name + formal problem definition
docs/plans/2026-02-13-hamiltonian-cycle-model.md	Adds implementation plan document for the model

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.

[Copilot]

The problem definition uses C in the objective (sum_(e in C) w(e)) but doesn't define what C is. Please define C (e.g., C ⊆ E is the edge set of a Hamiltonian cycle / a cycle visiting every vertex exactly once) so the statement is self-contained and unambiguous.

Suggested change

	Given an undirected graph $G=(V,E)$ with edge weights $w: E -> RR$, find a cycle visiting every vertex exactly once that minimizes $sum_(e in C) w(e)$.
	Given an undirected graph $G=(V,E)$ with edge weights $w: E -> RR$, find an edge set $C subset.eq E$ that forms a cycle visiting every vertex exactly once and minimizes $sum_(e in C) w(e)$.

[GiggleLiu]

Weighted HamiltonianCycle is equivalent to TravelingSalesman problem. Please rename.