The interval number of a graph G is the minimum k such that one can assign to each vertex of G a union of k intervals on the real line, such that G is the intersection graph of these sets, i.e., two vertices are adjacent in G if and only if the corresponding sets of intervals have non-empty intersection.

Scheinerman and West (1983) [14] proved that the interval number of any planar graph is at most 3. However the original proof has a flaw. We give a different and shorter proof of this result.

中文翻译：

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平面图的间隔数最多为3

图G的间隔数是最小值k，因此可以为G的每个顶点分配实线上的k个间隔的并集，从而G是这些集合的交集图，即，两个顶点在G中相邻当且仅当对应的间隔集具有非空交集时。

Scheinerman and West（1983）[14]证明任何平面图的间隔数最多为3。但是原始证明存在缺陷。我们对此结果给出了不同且简短的证明。