Low-cost genome sequencing gives unprecedented complete information about the genetic structure of populations, and a population graph captures the variations between many individuals of a population. Recently, Marcus et al. proposed to use a compressed de Bruijn graph for representing an entire population of genomes. They devised an O(n log g) time algorithm called splitMEM that constructs this graph directly (i.e. without using the uncompressed de Bruijn graph) based on a suffix tree, where n is the total length of the genomes and g is the length of the longest genome. Since the applicability of their algorithm is limited to rather small datasets, there is a strong need for space-efficient construction algorithms.