The existence of a four-dimensional cycle-free order is proved. This answers a question of Ma and Spinrad. Two similar problems are also discussed.

/pdf/the-dimension-of-cycle-free-orders-1cb7r3otyt.pdf

The Dimension of Cycle-Free Orders

Generalized perfect graphs: characterizations and inversion

Interval orders and interval graphs, Fishburn P.C. (Ed.). Wiley, New York (1985), 215, $33.50

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Interval orders and interval graphs, Fishburn P.C. (Ed.). Wiley, New York (1985), 215, $33.50