On dimensional properties of graphs. (English) Zbl 0675.05054

Summary: A dimensional property of graphs is a property P such that every graph G is the intersection of graphs having property P. If P is a dimensional property, we describe a general method for computing the least integer k so that G is the intersection of k graphs having property P. We give simple applications of the method to computing the boxicity, the cubicity, the circular dimension, the rigid circuit dimension, and the overlap dimension, and mention connections to other concepts such as the threshold dimension.


05C75 Structural characterization of families of graphs
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