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intersection graph; intersection dimension
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.
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