Posets with interval upper bound graphs

Competition graphs of transitive acyclic digraphs are strict upper bound graphs. This paper characterizes those posets, which can be considered transitive acyclic digraphs, which have upper bound graphs that are interval graphs. The results proved here may shed some light on the open question of those digraphs which have interval competition graphs.This material is taken from Chapter 3 of my (maiden name Diny) PhD Dissertation.