Dimension of Restricted Classes of Interval Orders

Mitchel T. Keller, Ann N. Trenk, Stephen J. Young

Published 2020-04-17Version 1

Rabinovitch showed in 1978 that the interval orders having a representation consisting of only closed unit intervals have order dimension at most 3. This article shows that the same dimension bound applies to two other classes of posets: those having a representation consisting of unit intervals (but with a mixture of open and closed intervals allowed) and those having a representation consisting of closed intervals with lengths in $\{0,1\}$.