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Mat. Zametki, 1974, Volume 16, Issue 6, Pages 957–968 (Mi mz7538)  

On elementary theories of graphs and Abelian loops

D. Ya. Kesel'man

Siberian Energy Institute

Abstract: The algorithmic decidability of elementary theories of certain classes of graphs, such as homogeneous, planar, bipartite planar, and critical nonplanar, is discussed. For the first three classes we prove the undecidability of elementary theories, and for the last, decidability with a supplementary predicate. We also prove the undecidability of theory of Abelian loops by an interpretation in it of theory of bipartite homogeneous 3rd degree graphs.

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English version:
Mathematical Notes, 1974, 16:6, 1167–1171

Bibliographic databases:

UDC: 519.4
Received: 30.07.1973

Citation: D. Ya. Kesel'man, “On elementary theories of graphs and Abelian loops”, Mat. Zametki, 16:6 (1974), 957–968; Math. Notes, 16:6 (1974), 1167–1171

Citation in format AMSBIB
\Bibitem{Kes74}
\by D.~Ya.~Kesel'man
\paper On elementary theories of graphs and Abelian loops
\jour Mat. Zametki
\yr 1974
\vol 16
\issue 6
\pages 957--968
\mathnet{http://mi.mathnet.ru/mz7538}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=371742}
\zmath{https://zbmath.org/?q=an:0311.02063}
\transl
\jour Math. Notes
\yr 1974
\vol 16
\issue 6
\pages 1167--1171
\crossref{https://doi.org/10.1007/BF01098445}


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