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.
@article{118754,
author = {Petr Hlin\v en\'y and Ale\v s Kub\v ena},
title = {A note on intersection dimensions of graph classes},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {36},
year = {1995},
pages = {255-261},
zbl = {0838.05042},
mrnumber = {1357527},
language = {en},
url = {http://dml.mathdoc.fr/item/118754}
}
Hliněný, Petr; Kuběna, Aleš. A note on intersection dimensions of graph classes. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 255-261. http://gdmltest.u-ga.fr/item/118754/
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