A note on Cops and Robbers, independence number, domination number and diameter

02/25/2022

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by   Jan Petr, et al.

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We study relations between diameter D(G), domination number γ(G), independence number α(G) and cop number c(G) of a connected graph G, showing (i.) c(G) ≤α(G)-⌊D(G)-3/2⌋, and (ii.) c(G) ≤γ (G) - D(G)/3 + O (√(D(G))).