Abstract: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.: {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.
Keywords: intersection graph, intersection dimension
AMS Subject Classification: 05C10, 05C30