On ordered graphs and graph orderings
The main result of this paper is: For every oriented graph \(\vec G\) with in-degree for every vertex at least 2 there is no graph \(H\) such that every strong orientation \(\vec H\) of \(H\) contains a copy of \(\vec G\). This disproves a conjecture of \textit{M. Cochand} and \textit{P. Duchet} [Algorithms Comb. 8, 39-46 (1989; Zbl 0698.05055)]. The author also discusses the relationship of the above result and similar results with Ramsey theory.
scientific article; zbMATH DE number 612436