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 Arcadi4/nerdy --skill matchings-in-biparite-graphsgit clone --depth 1 https://github.com/Arcadi4/nerdyWrote 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/arcadi4/nerdy/matchings-in-biparite-graphs)<a href="https://agentmods.dev/skills/arcadi4/nerdy/matchings-in-biparite-graphs"><img src="https://agentmods.dev/badge/skills/arcadi4/nerdy/matchings-in-biparite-graphs/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/arcadi4/nerdy/matchings-in-biparite-graphs"><img src="https://agentmods.dev/badge/skills/arcadi4/nerdy/matchings-in-biparite-graphs.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 | $0.00055 | $0.04740 |
| Opus 5.5 | $0.00022 | $0.01896 |
| Sonnet 5.5 | $0.00011 | $0.00948 |
| Haiku 4.5 | $0.00006 | $0.00474 |
Grade A, and why
matchings-in-biparite-graphs 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 1mo 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 — 399 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Matchings in Bipartite Graphs
Overview
Matching answers are dual-structure answers: first decide whether the task is cardinality matching, stable preference matching, or weighted assignment, then use the certificate that belongs to that model. Augmenting paths certify maximum cardinality, no blocking pair certifies stability, and feasible labels plus equality edges certify optimal weighted assignments.
Core principle: do not collapse the chapter into a generic max-flow reduction. Preserve the matching-specific alternating-path, rejection, and labeling proof moves, then translate textbook pseudocode into implementation contracts only when the input model justifies it.
Shared CLRS Conventions
- Follow the parent
clrsskill for mathematical formatting: every formula, inequality, set expression, slack definition, or asymptotic bound belongs in a display LaTeX block, never in prose, headings, table cells, or inline code spans. - Use
elementary-graph-algorithmsfor ordinary graph representation, breadth-first search, depth-first search, and transpose traversal mechanics. - Use
maximum-flowwhen the requested deliverable is a flow-network reduction or an integrality proof. Use this skill when the requested deliverable is a matching algorithm, matching theorem, stable-matching proof, or assignment-labeling argument. - Keep quick-reference tables verbal. Put all symbolic definitions and running times in display blocks near the table.
- State which side of the bipartition proposes, which side is optimized, and whether the matching is cardinality, stable, or weighted before naming an algorithm.
- Start directly with the polished answer. The first visible line must be a domain heading or a substantive matching sentence, not a process note. Do not include meta preambles such as “checking formatting,” “evaluating complexity,” “evaluating the skill,” “I’m thinking,” “displaying complexity,” “scenario answer,” or “finalizing the presentation,” because those are common places for forbidden inline formulas and session narration to leak. If a draft starts with one of those phrases, delete the preamble before answering.
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.
- 1mo ago First seen · 399 lines · 55 tokens per session scan A 824d9cd6fac4
matchings-in-biparite-graphs is a skill published in the GitHub repository Arcadi4/nerdy (6 stars, last pushed 6mo ago), licensed MIT. It adds 55 tokens to every session and 4,740 once invoked, about $0.0002 per session on Opus 5.5. 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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