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Determining whether a given graph = (,) is an interval graph can be done in (| | + | |) time by seeking an ordering of the maximal cliques of that is consecutive with respect to vertex inclusion. Many of the known algorithms for this problem work in this way, although it is also possible to recognize interval graphs in linear time without using ...
An interval is said to be bounded, if it is both left- and right-bounded; and is said to be unbounded otherwise. Intervals that are bounded at only one end are said to be half-bounded. The empty set is bounded, and the set of all reals is the only interval that is unbounded at both ends. Bounded intervals are also commonly known as finite ...
An independent set in an interval graph is just a set of non-overlapping intervals. The problem of finding maximum independent sets in interval graphs has been studied, for example, in the context of job scheduling : given a set of jobs that has to be executed on a computer, find a maximum set of jobs that can be executed without interfering ...
An indifference graph, formed from a set of points on the real line by connecting pairs of points whose distance is at most one. In graph theory, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting two vertices by an edge when their numbers are within one unit of each other. [1]
An RR tachograph is a graph of the numerical value of the RR-interval versus time. In the context of RR tachography, a Poincaré plot is a graph of RR(n) on the x-axis versus RR(n + 1) (the succeeding RR interval) on the y-axis, i.e. one takes a sequence of intervals and plots each interval against the following interval. [3]
The subclass of interval orders obtained by restricting the intervals to those of unit length, so they all have the form (, +), is precisely the semiorders. The complement of the comparability graph of an interval order ( X {\displaystyle X} , ≤) is the interval graph ( X , ∩ ) {\displaystyle (X,\cap )} .
Interval graphs and chordal graphs also have at most n maximal cliques, even though they are not always sparse graphs. The number of maximal independent sets in n-vertex cycle graphs is given by the Perrin numbers, and the number of maximal independent sets in n-vertex path graphs is given by the Padovan sequence. [6]
Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".