On Woodall's Interval Problem

Abstract For each k > 1, a sequence of 4(k − 1) − [log2 (k − 1)] sets (layers) of disjoint intervals in R is constructed, such that every interval overlaps at least one interval in each preceding layer and no point of R belongs to more than k layers. This improves a construction of Woodall. The approach is by way of the related “saturation” or “scope” problem.