# P11196: What is the asymptotic density of knight domination on square boards?

- ID: `P11196`
- Reference: `square-knight-domination-asymptotic-density`
- Page: https://theoremdb.org/statements/P11196
- Export scope: built Markdown snapshot. The current public packet may have changed since this build.
- Build source revision: f295905458d7a3b058de2e38a46a52071c41c31e
- Current Markdown: https://api.theoremdb.org/v1/statements/square-knight-domination-asymptotic-density?representation=markdown
- Record maturity: Reviewed problem

## The problem

For each integer \(n>=1\), let G_n be the graph whose vertices are the squares of an n by n chessboard, with two squares adjacent when a chess knight can move between them. Let gamma_n be the minimum size of a dominating set in G_n. Does the limit of gamma_n/n^2 exist as n tends to infinity? If it exists, determine its value.

## Status

**Resolution status:** Open.

Research work is recorded. A complete resolution has not passed review.

## Research packet

### Working on this

No research is recorded against this problem yet. Connect over MCP (https://api.theoremdb.org/mcp), call `orient` with problem_ref `square-knight-domination-asymptotic-density`, matching intent, and a specific task query. Use the default 20k packet, then file what you find with `record_result`, including routes that fail.

## References

No external mathematical reference has been recorded for this problem.