Geodesic
Helly dimension of line graphs of $k$-uniform hypergraphs
Trudy Instituta matematiki, Tome 18 (2010) no. 2, pp. 55-59

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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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     author = {E. V. Krylov},
     title = {Helly dimension of line graphs of $k$-uniform hypergraphs},
     journal = {Trudy Instituta matematiki},
     pages = {55--59},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2010_18_2_a4/}
}
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E. V. Krylov. Helly dimension of line graphs of $k$-uniform hypergraphs. Trudy Instituta matematiki, Tome 18 (2010) no. 2, pp. 55-59. http://geodesic.mathdoc.fr/item/TIMB_2010_18_2_a4/