Doklady Mathematics

, Volume 98, Issue 3, pp 638–640 | Cite as

A Disproof the Le Bars Conjecture about the Zero–One Law for Existential Monadic Second-Order Sentences

  • M. E. ZhukovskiiEmail author
  • S. N. Popova


The Le Bars conjecture (2001) states that the binomial random graph G(n, \(\frac{1}{2}\)) obeys the zero–one law for existential monadic sentences with two first-order variables. This conjecture is disproved. Moreover, it is proved that there exists an existential monadic sentence with a single monadic variable and two first-order variables whose truth probability does not converge.


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Moscow Institute of Physics and Technology (State University)Dolgoprudnyi, Moscow oblastRussia
  2. 2.Caucasus Mathematical CenterAdyghe State UniversityMaikop, Maikop, Republic of AdygeaRussia

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