In mathematics, especially order theory, the interval order for a collection of intervals on the real line is the partial order corresponding to their left-to-right precedence relation—one interval, I1, being considered less than another, I2, if I1 is completely to the left of I2. More formally, a poset is an interval order if and only if there exists a bijection from to a set of real intervals, so, such that for any we have in exactly when .
An interval order defined by unit intervals is a semiorder.
The complement of the comparability graph of an interval order (, ≤) is the interval graph .
Interval orders should not be confused with the interval-containment orders, which are the containment orders on intervals on the real line (equivalently, the orders of dimension ≤ 2).
Read more about Interval Order: Interval Dimension
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