Definition
Let {I1, I2, ..., In} ⊂ P(R) be a set of intervals.
The corresponding interval graph is G = (V, E), where
- V = {I1, I2, ..., In}, and
- {Iα, Iβ} ∈ E if and only if Iα ∩ Iβ ≠ ∅.
From this construction one can verify a common property held by all interval graphs. That is, graph G is an interval graph if and only if the maximal cliques of G can be ordered M1, M2, ..., Mk such that for any v ∈ Mi ∩ Mk, where i < k, it is also the case that v ∈ Mj for any Mj, i ≤ j ≤ k.
Read more about this topic: Interval Graph
Famous quotes containing the word definition:
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.”
—François, Duc De La Rochefoucauld (1613–1680)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)