graph-coloring

graph-coloring is a skill for Claude Code from hajibabaie/combinatorial-optimization-skills. It costs 133 tokens per session (10,430 once invoked), scanned A, original, MIT.

A toolkit for graph coloring: assigning colors to connected points so neighboring points have different colors while using as few colors as possible. A graph is a set of points and links between them.

In plain words
What is it for?
Use it for register allocation, frequency assignment, exam timetables, and other problems involving conflicts between items.
Why use it?
It helps solve scheduling and assignment problems where nearby or conflicting items cannot share a color. It can compare exact methods with faster estimates and report how close a result is to the best possible one.

Skill for Claude Code

Written for Claude Code: shipped in a Claude Code plugin.

Part of the combinatorial-optimization plugin — 76 skills shipped together

Good fit Use it for register allocation, frequency assignment, exam timetables, and other problems involving conflicts between items.

Compare 6 skills from other repositories ↓
Install with agentmods
npx agentmods add skills/hajibabaie/combinatorial-optimization-skills/graph-coloring
Install

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.

Any agent
npx skills add hajibabaie/combinatorial-optimization-skills --skill graph-coloring
Clone the repo
git clone --depth 1 https://github.com/hajibabaie/combinatorial-optimization-skills

Made for: Claude Code.

Or install combinatorial-optimization, the plugin that ships this one along with the rest of its 76 skills.

Wrote 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.

agentmods badge for graph-coloring

README.md
[![agentmods](https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/graph-coloring/github.svg)](https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/graph-coloring)
Your own site
<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.

agentmods 80×15 button for graph-coloring

Your own site · 80×15
<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>
Per session 133 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 10,430 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. A grade says what 26 rules found in the file — not that it is safe.
Origin original No closer match found in the catalogue.
Token cost

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.

ModelPer sessionOnce 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

Measured 8d ago against content hash 940d783f1e75, method: parsed. Prices are Anthropic first-party input rates as of 2026-09-08, from the pricing page.

Security

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.

skills/graph-coloring/SKILL.md · 668 lines

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 .col file? 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.

Read the full file on GitHub · 668 lines

Changes

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.

  1. 8d ago First seen · 668 lines · 133 tokens per session scan A 940d783f1e75

Subscribe to this mod's changes

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.

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