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Gy{\\'a}rf{\\'a}s, Problems from the world surrounding perfect graphs, {\\em Zastowania Matematyki Applicationes Mathematicae}, 19:413--441, 1987]. For a $\\chi$-bounded class $\\cal C$, is the class $\\bar{C}$ $\\chi$-bounded (where $\\bar{\\cal C}$ is the class of graphs formed by the complements of graphs from $\\cal C$)? 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