Extending Greene's theorem to directed graphs

Abstract

The purpose of this note is to prove a theorem on acyclic digraphs, conjectured by Linial (J. Combin. Theory Ser. A, 30 (1981), 331-334), which includes Greene's theorem (J. Combin. Theory Ser. A, 20 (1976), 69-79) on decompositions of a partially ordered set into antichains. © 1983.