Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Matematicheskie Zametki, 1997, Volume 61, Issue 6, Pages 873–883
DOI: https://doi.org/10.4213/mzm1571
(Mi mzm1571)
 

Estimates of the independence number of a hypergraph and the Ryser conjecture

V. E. Tarakanov

Steklov Mathematical Institute, Russian Academy of Sciences
References:
Abstract: Consider a hypergraph $H$ with $n$ vertices and $m$ edges. Suppose that its edges contain at most $r$ vertices, $r\ge2$, and the degrees of its vertices do not exceed $\delta\ge2$. Let $\tau(H)$ be the transversal number of the graph $H$ and $\mu(H)$ be its independence number, i.e., the maximal number of pairwise nonintersecting edges containing $r$ vertices. We strengthen the known estimate $\mu\ge(\delta n-(r-1)m)/(\delta r-r+1)$ for the case in which $H$ is a pseudograph and the maximal degree of its vertices equals $\Delta$, $2\delta-2\ge\Delta$ (there is a similar result for graphs). Then we use the sharpened estimate to prove the well known Ryser conjecture on $r$-partite $r$-uniform hypergraphs $H$: this conjecture states that $\tau(H)\le(r-1)\mu(H)$, and we prove it for $\delta$-regular $H$, where $2\le\delta\le r-1$.
Received: 19.09.1996
English version:
Mathematical Notes, 1997, Volume 61, Issue 6, Pages 731–738
DOI: https://doi.org/10.1007/BF02361215
Bibliographic databases:
Document Type: Article
UDC: 519.17
Language: Russian
Citation: V. E. Tarakanov, “Estimates of the independence number of a hypergraph and the Ryser conjecture”, Mat. Zametki, 61:6 (1997), 873–883; Math. Notes, 61:6 (1997), 731–738
Citation in format AMSBIB
\Bibitem{Tar97}
\by V.~E.~Tarakanov
\paper Estimates of the independence number of a hypergraph and the Ryser conjecture
\jour Mat. Zametki
\yr 1997
\vol 61
\issue 6
\pages 873--883
\mathnet{http://mi.mathnet.ru/mzm1571}
\crossref{https://doi.org/10.4213/mzm1571}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1629809}
\zmath{https://zbmath.org/?q=an:0914.05054}
\elib{https://elibrary.ru/item.asp?id=13250227}
\transl
\jour Math. Notes
\yr 1997
\vol 61
\issue 6
\pages 731--738
\crossref{https://doi.org/10.1007/BF02361215}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1997YE52200027}
Linking options:
  • https://www.mathnet.ru/eng/mzm1571
  • https://doi.org/10.4213/mzm1571
  • https://www.mathnet.ru/eng/mzm/v61/i6/p873
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024