What is the asymptotic density of knight domination on square boards?
TheoremDB P11196 · combinatorics
Inferred from the community field; finer classification has not been reviewed.
Problem statement
For each integer , 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.
Lean 4
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Background
Additional formulation recorded by the source
For gamma_n=gamma(G_n), determine whether lim_{n->infinity} gamma_n/n^2 exists and evaluate it if it does.
Progress & source assessment
Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
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