, Volume 8, Issue 1, pp 49-61

Cycle-free partial orders and chordal comparability graphs

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Abstract

This paper studies a number of problems on cycle-free partial orders and chordal comparability graphs. The dimension of a cycle-free partial order is shown to be at most 4. A linear time algorithm is presented for determining whether a chordal directed graph is transitive, which yields an O(n 2) algorithm for recognizing chordal comparability graphs. An algorithm is presented for determining whether the transitive closure of a digraph is a cycle-free partial order in O(n+m t)time, where m tis the number of edges in the transitive closure.

Communicated by I. Rival