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
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