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}.
Published: September 23, 2022
Citation
Keller M.T., A. Trenk, and S.J. Young. 2022.Dimension of Restricted Classes of Interval Orders.Graphs and Combinatorics 38, no. 5:Art. No. 137.PNNL-SA-152654.doi:10.1007/s00373-022-02543-6