Geodesic
A note on intersection dimensions of graph classes
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 2, pp. 255-261 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The intersection dimension of a graph $G$ with respect to a class $\Cal A$ of graphs is the minimum $k$ such that $G$ is the intersection of some $k$ graphs on the vertex set $V(G)$ belonging to $\Cal A$. In this paper we follow [\,Kratochv'\i l J., Tuza Z.: {\sl Intersection dimensions of graph classes\/}, Graphs and Combinatorics 10 (1994), 159--168\,] and show that for some pairs of graph classes $\Cal A$, $\Cal B$ the intersection dimension of graphs from $\Cal B$ with respect to $\Cal A$ is unbounded.
The intersection dimension of a graph $G$ with respect to a class $\Cal A$ of graphs is the minimum $k$ such that $G$ is the intersection of some $k$ graphs on the vertex set $V(G)$ belonging to $\Cal A$. In this paper we follow [\,Kratochv'\i l J., Tuza Z.: {\sl Intersection dimensions of graph classes\/}, Graphs and Combinatorics 10 (1994), 159--168\,] and show that for some pairs of graph classes $\Cal A$, $\Cal B$ the intersection dimension of graphs from $\Cal B$ with respect to $\Cal A$ is unbounded.
Classification : 05C10, 05C30, 05C70, 05C75
Keywords: intersection graph; intersection dimension 
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     title = {A note on intersection dimensions of graph classes},
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     pages = {255--261},
     year = {1995},
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Hliněný, Petr; Kuběna, Aleš. A note on intersection dimensions of graph classes. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 2, pp. 255-261. http://geodesic.mathdoc.fr/item/CMUC_1995_36_2_a5/