Abstract
A set of data has a Guttman scale if and only if a corresponding graph is a threshold graph. In this paper we relate the concepts of disjunctive and conjuctive Guttman scales, and biorder dimension to the threshold dimension of a graph. For those graphical properties that can be tested in polynomial time, the comparable Guttman scaling techniques can be performed in polynomial time. Fast algorithms are provided for computing a Guttman scale, and the conjunctive and disjunctive dimension of data with no 3-crowns. We define an extended Guttman scale to indicate strength of agreement, dominance, etc., and show that this, too, exists if and only if a particular graph is a threshold graph.
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