The (≤p)-inversion diameter of any graph G is at most ceil(|E(G)| / floor(p/2)) + Ψ_p, where Ψ_p satisfies (p/4 - 3/2) ≤ Ψ_p ≤ p²/2, with improved linear-in-n bounds for trees and planar graphs.
Invertibility of digraphs and tournaments.SIAM Journal on Dis- crete Mathematics, 38(1):327–347
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On the $(\leq p)$-inversion diameter of oriented graphs
The (≤p)-inversion diameter of any graph G is at most ceil(|E(G)| / floor(p/2)) + Ψ_p, where Ψ_p satisfies (p/4 - 3/2) ≤ Ψ_p ≤ p²/2, with improved linear-in-n bounds for trees and planar graphs.