Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Claim. O. Pretzel, A non-covering graph of girth six, Discrete Math. 63 (1987), no. 2--3, 241--244. The author's summary of the paper, as zbMATH Open prints it (Zbl 0651.05046), reads: "We construct a graph of girth 6 that cannot be oriented as the diagram of an ordered set and discuss the reasons why this particular construction cannot be extended to produce examples of larger girth." The paper's construction itself is not stated here. The journal record gives the year and no day, so this page carries the first of January.
Depends on. The Formulation of Problem 1006, where the orientations asked for are those of the graph as the diagram (Hasse diagram) of an ordered set, so a graph of girth at least five that is not a cover graph answers the question no.
Acceptance. None listed. The paper appeared in Discrete Mathematics 63 (1987), but only the author's summary on zbMATH Open was available to this page, so the theorem is stated from that summary and refereed evidence is not listed. The site's commentary credits the disproof to Nešetřil and Rödl, whose earlier probabilistic construction is on [[problems/extremal_graph_theory/E1006/claims/1978_11_01_nesetril_rodl|their page]], and does not cite this paper, so no curator acceptance is listed. The paper's proof is not reproduced here.