---

Claim. V. Neumann-Lara, A short proof of a theorem of Reid and Parker on tournaments, Graphs Combin. 10 (1994), no. 2--4, 363--366, gives a shorter proof of Reid and Parker's theorem that for $k\ge5$ and $n\ge7\cdot2^{k-4}$ every tournament of order $n$ contains a transitive subtournament of order $k$; this is the paper's result as the zbMATH review (Zbl 0811.05028, by B. Alspach) states it. At $k=5$ every tournament on $14$ vertices contains a transitive subtournament on $5$ vertices, so $f(14)\ge5$ while the formula of Problem 1216 gives $\lfloor\log_214\rfloor+1=4$, and the answer to the question is no. The theorem reproved is Corollary 1 of Reid and Parker, recorded on their claim page; this page records the independent proof.

Depends on. Nothing in this wiki; the proof is the paper's own.

Source. The page is dated by the issue month of the journal record (Graphs and Combinatorics 10, no. 2--4, June 1994, per Crossref); the day in the page name is a placeholder.

Acceptance. Refereed: Graphs and Combinatorics 10 (1994), no. 2--4, 363--366. The site's commentary does not cite this paper, so no reviewed evidence is listed. The proof is not checked in this corpus.