Novák, Vítězslav On some minimal problem. (English) Zbl 0554.06003 Arch. Math., Brno 20, 95-99 (1984). It is known [N. Megiddo, Bull. Am. Math. Soc. 82, 274-276 (1976; Zbl 0361.06001)] that not any cyclic order has a linear extension. The paper deals with the problem of a minimal integer n such that there exists a cyclic order on an n-element set which has no linear extension; by N. Megiddo, \(n\leq 13\). The paper contains an example improving this estimation for \(n\leq 10\). Reviewer: I.Chajda MSC: 06A06 Partial orders, general 05A20 Combinatorial inequalities Keywords:cyclic order; linear extension Citations:Zbl 0361.06001 PDFBibTeX XMLCite \textit{V. Novák}, Arch. Math., Brno 20, 95--99 (1984; Zbl 0554.06003) Full Text: EuDML