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On some minimal problem. (English) Zbl 0554.06003
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, n13. The paper contains an example improving this estimation for n10.
Reviewer: I.Chajda
MSC:
06A06Partial order
05A20Combinatorial inequalities