A Note on Undirected Graphs Realizable as P.O. Sets

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Abstract
Let (P, ≥) be a p.o. set. The basis graph of (P, ≥) is defined to be the directed graph whose vertex set is P and in which the ordered pair 〈a, b〉 is an edge if and only if b covers a in (P, ≥).Let D be a directed graph. All graphs considered in this note are finite and are free of loops and multiple edges.

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