Claims

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1999_01_01_schipperus: Schipperus (thesis 1999, Ann. Pure Appl. Logic 2010) proved that the ordinal omega^(omega^2) satisfies the arrow relation for a triangle but not for a complete graph on six vertices, answering the question no.

1999_07_01_darby: Darby (J. Combin. Theory Ser. B, 1999) is credited, independently of Schipperus, with the counterexample omega^(omega^2), a partition ordinal that fails the arrow relation at six; his paper is not held here.

2000_09_01_larson: Larson (J. Symbolic Logic, 2000) proved that omega^(omega^2) fails the arrow relation for a complete graph on five vertices, sharpening the counterexample of Schipperus and Darby; the site's curator credits it.

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