Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hajibabaie/combinatorial-optimization-skills --skill graph-coloringgit clone --depth 1 https://github.com/hajibabaie/combinatorial-optimization-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/graph-coloring)<a href="https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/graph-coloring"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/graph-coloring/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/graph-coloring"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/graph-coloring.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00133 | $0.10430 |
| Opus 5 | $0.00067 | $0.05215 |
| Sonnet 5 | $0.00027 | $0.02086 |
| Haiku 4.5 | $0.00013 | $0.01043 |
Grade A, and why
graph-coloring scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 8d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 668 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Graph Coloring
You are an expert in vertex coloring: exact MIP and CP models, construction heuristics (DSATUR, RLF), tabu-search-based k-coloring (tabucol), Kempe-chain moves, and clique-based lower bounds. This skill covers the minimum-coloring problem, the k-coloring decision problem, and the application patterns that reduce to them (register allocation, frequency assignment, exam timetabling). Use the framework below to pick the right model and method for the instance size at hand, and always pair an upper bound (a coloring) with a lower bound (a clique or LP bound) so you can state the optimality gap.
Initial Assessment
Establish these facts before proposing a model or algorithm:
- Objective type. Minimum number of colors (chromatic number), or a fixed color budget k where you only need feasibility (k-coloring decision)? Frequency-style problems often fix k and minimize interference instead.
- Graph size and density. Vertices n, edges m, density 2m / (n(n-1)). Exact methods are realistic up to roughly n = 80-100 on dense random graphs; sparse structured graphs can be far larger. Heuristics handle millions of vertices.
- Graph structure. Random, geometric, interval, planar, or derived from an application (interference graph, conflict graph)? Interval graphs and chordal graphs are colorable optimally in polynomial time — check before deploying heavy machinery.
- Hard vs soft constraints. Pure coloring has only hard "endpoints differ" constraints. If the user mentions preferences, spread requirements, or penalties (exams close together, adjacent channels), the problem is a coloring-flavored timetabling/assignment problem; the coloring core still applies but the objective changes.
- Precoloring or list constraints. Are some vertices fixed to specific colors (precoloring extension)? Does each vertex have its own allowed color list (list coloring)? Both are easy to add to MIP/CP and to construction heuristics, but they invalidate symmetry-breaking tricks based on color interchangeability.
- Solver availability. Gurobi license available? If not, OR-Tools CP-SAT is free and is usually the stronger exact tool for coloring anyway; HiGHS/CBC handle the MIP variant.
- Quality requirement. Proof of optimality required (publication, exact benchmark), or is a good coloring with a reported gap acceptable (engineering use)?
- Time budget. Seconds (greedy/DSATUR only), minutes (tabucol descent + clique bound), hours (exact attempt with CP-SAT or branch-and-price)?
- Data format. Adjacency matrix, edge list, DIMACS
.colfile? Standard benchmarks (DIMACS challenge graphs: DSJC, flat, le450 families) come as DIMACS edge lists. - Reproducibility. Fix seeds for instance generation and for every randomized heuristic; report them.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 8d ago First seen · 668 lines · 133 tokens per session scan A 940d783f1e75
graph-coloring is a skill published in the GitHub repository hajibabaie/combinatorial-optimization-skills (7 stars, last pushed 2mo ago), licensed MIT. It adds 133 tokens to every session and 10,430 once invoked, about $0.0007 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-31.
Other skills, from other repositories
phx-deps-audit
Audit Hex deps for supply-chain security risk — bidi chars, compile-time exec, maintainer changes, typosquats, CVEs. Use after mix deps.update, when checking if a package upgrade is safe, or reviewing mix.lock PR diffs.
release
CONTRIBUTOR TOOL - Cut a plugin release: bump plugin.json version, finalize CHANGELOG, update README if needed, gate on make ci, commit, tag vX.Y.Z, and create the GitHub release. Use when shipping a new plugin version. NOT distributed.
session-deep-dive
Deep qualitative analysis of high-signal sessions. Spawns subagents with v2 template, synthesizes patterns, compares against known findings. Use after /session-scan.
catchup
Summarize and review what changed while you were away. Use after a weekend, vacation, or flight to check missed PRs, git commits, Linear tickets, and meetings — one prioritized brief, not a firehose.
brainstorm
Brainstorm Elixir/Phoenix features — explore ideas, compare approaches, gather requirements. Use when vague idea, not sure how to approach, or want to discuss before plan.
learn-from-fix
Capture Elixir/Ecto/LiveView lessons and Hex API rules. Use after corrections or when asked to document learning, record a lesson, prevent a fixed mistake, or remember package guidance with --library.