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Tr. Inst. Mat., 2010, Volume 18, Number 2, Pages 55–59 (Mi timb17)  

Helly dimension of line graphs of $k$-uniform hypergraphs

E. V. Krylov

Belarusian State University

Abstract: Dependencies of Helly and Krauz dimension are investigated ($r$-mino and line graphs of $k$-uniform hypergraphs, respectively). It is shown that intersection of $r$-mino and line graphs of $k$-uniform hypergraphs classes is not empty for any $r\ge k\ge 2$. It is proven that helly dimension can be computed in a polynomial time against krauz dimension and maximal vertex degree of graph. Boundaries of helly dimension in terms of krauz dimension are given. It is proven that “$kd_s(G)\le 3$” recognition problem is $NP$-complete in the $3$-mino class.

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Bibliographic databases:
UDC: 519.1
Received: 30.12.2009

Citation: E. V. Krylov, “Helly dimension of line graphs of $k$-uniform hypergraphs”, Tr. Inst. Mat., 18:2 (2010), 55–59

Citation in format AMSBIB
\Bibitem{Kry10}
\by E.~V.~Krylov
\paper Helly dimension of line graphs of $k$-uniform hypergraphs
\jour Tr. Inst. Mat.
\yr 2010
\vol 18
\issue 2
\pages 55--59
\mathnet{http://mi.mathnet.ru/timb17}
\zmath{https://zbmath.org/?q=an:05863490}


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