Linear-semiorders and their incomparability graphs

07/18/2019

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by   Asahi Takaoka, et al.

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A linear-interval order is the intersection of a linear order and an interval order. For this class of orders, several structural results have been shown. In this paper, we study a natural subclass of linear-interval orders. We call a partial order a linear-semiorder if it is the intersection of a linear order and a semiorder. We show a characterization of linear-semiorders in terms of linear extensions. This gives a vertex ordering characterization of their incomparability graphs. We also show that being a linear-semiorder is a comparability invariant.