A note on an embedding problem in transitive tournaments (Q965937)

Let \(TT_n\) be a transitive tournament on n vertices. It is known [\textit{A. Görlich}, \textit{M. Pilśniak}, and \textit{M. Woźniak}, Graphs Comb. 22, No.\,2, 233--239 (2006; Zbl 1100.05074)] that for any acyclic oriented graph \(\vec G\) of order n and size not greater than \(3(n-1)/4\), two graphs isomorphic to \(\vec G\) are arc-disjoint subgraphs of \(TT_n\). In this paper, authors consider the problem of embedding of acyclic oriented graphs into their complements in transitive tournaments. They show that any acyclic oriented graph \(\vec G\) of size at most \(2(n-1)/3\) is embeddable into all its complements in \(TT_n\). Moreover, this bound is generally the best possible.