Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports]
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sib. Èlektron. Mat. Izv.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 137–147
DOI: https://doi.org/10.17377/semi.2016.13.012
(Mi semr662)
 

This article is cited in 2 scientific papers (total in 2 papers)

Mathematical logic, algebra and number theory

On axiomatizability of hereditary classes of graphs and matroids

A. V. Iliev

Sobolev Institute of Mathematics, Pevtsova str., 13, 644043, Omsk, Russia
Full-text PDF (166 kB) Citations (2)
References:
Abstract: In the paper, hereditary classes of graphs and matroids are studied by means of the model theory. The problems of first-order axiomatizability of some classes of graphs and matroids are considered. The criterion of axiomatizability of monotone hereditary classes of graphs defined by forbidden noninduced subgraphs is proved. Necessary and sufficient conditions of universal and finite axiomatizability of the monotone hereditary classes of graphs are obtained. It is proved that the class of matroids of fixed rank k is finitely axiomatizabile, as well as two hereditary classes of matroids of bounded rank — the class of matroids of rank not exeeding $k$ and the class of partition matroids of rank not exeeding $k$. It is also shown that the hereditary class of matroids of finite rank is nonaxiomatizable.
Keywords: axiomatizability, graph, matroid, hereditary class.
Received December 21, 2015, published March 11, 2016
Bibliographic databases:
Document Type: Article
UDC: 510.67, 519.17
MSC: 03C48, 05B35, 05C63
Language: Russian
Citation: A. V. Iliev, “On axiomatizability of hereditary classes of graphs and matroids”, Sib. Èlektron. Mat. Izv., 13 (2016), 137–147
Citation in format AMSBIB
\Bibitem{Ile16}
\by A.~V.~Iliev
\paper On axiomatizability of hereditary classes of graphs and matroids
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 137--147
\mathnet{http://mi.mathnet.ru/semr662}
\crossref{https://doi.org/10.17377/semi.2016.13.012}
Linking options:
  • https://www.mathnet.ru/eng/semr662
  • https://www.mathnet.ru/eng/semr/v13/p137
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Statistics & downloads:
    Abstract page:201
    Full-text PDF :61
    References:69
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024