[#P11196] What is the asymptotic density of knight domination on square boards?
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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.
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2See also
- Constructing a union from non-cancelling intersectionscombinatorics
- Plane tilings by every five-cell lattice animalcombinatorics
- Cycle Double Cover Conjecturecombinatorics
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“What is the asymptotic density of knight domination on square boards?.” TheoremDB. P11196. Problem statement; statement identity tdbc1:5588c26d304edb7eef2f44d27c1a9a6fc3631521e7ed59f79087cad3c2cf44fe; statement text SHA-256 b28f4929c9b514ff0d175553c6a2c6197e5a398e9e7c7e166afe276c470e77ae. https://theoremdb.org/statement/?ref=P11196
@misc{theoremdb-problem-b28f4929c9b514ff0d175553c6a2c6197e5a398e9e7c7e166afe276c470e77ae,
title = {{What is the asymptotic density of knight domination on square boards?}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:5588c26d304edb7eef2f44d27c1a9a6fc3631521e7ed59f79087cad3c2cf44fe; statement text SHA-256 b28f4929c9b514ff0d175553c6a2c6197e5a398e9e7c7e166afe276c470e77ae},
url = {https://theoremdb.org/statement/?ref=P11196}
}Plain text: Built Markdown snapshot
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