On dimensional properties of graphs

A dimensional property of graphs is a propertyP such that every graphG is the intersection of graphs having propertyP. IfP is a dimensional property, we describe a general method for computing the least integerk so thatG is the intersection ofk graphs having propertyP. 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.

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