Abstract
A directed graph is semi-transitive if and only if it is acyclic and for any directed path u1→u2→⋯→ut, t≥2, either there is no edge from u1 to ut or all edges ui→uj exist for 1≤i<j≤t. An undirected graph is semi-transitive if it admits a semi-transitive orientation. Recognizing semi-transitive orientability of a graph is an NP-complete problem.A split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Semi-transitive orientability of split graphs was recently studied in a series of papers in the literature. The main result in this paper is proving that recognition of semi-transitive orientability of split graphs can be done in a polynomial time.
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