A constructive lower bound w(s) ≥ 4^s/(2048 s^{5/2}) proves sup_s w(s)^{1/s} = 4 and yields cc(\bar{P_n}) = cc(\bar{C_n}) = log_2 n + Θ(log_2 log_2 n).
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Kohayakawa's conjecture and clique coverings of complements of paths and cycles
A constructive lower bound w(s) ≥ 4^s/(2048 s^{5/2}) proves sup_s w(s)^{1/s} = 4 and yields cc(\bar{P_n}) = cc(\bar{C_n}) = log_2 n + Θ(log_2 log_2 n).