The interval number of a planar graph is at most three

Abstract 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.