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Ongoing developments in genome sequencing have caused a fundamental paradigm shift in the field in recent years. With ever lower sequencing costs, projects are no longer limited by available raw data, but rather by computational demands. The high complexity of eukaryotic genomes in concordance with increasing data sizes creates unique demands on methods to assemble full genomes. We describe a new approach to assemble genomes from a combination of low-coverage short and long reads. LazyB starts from a bipartite overlap graph between long reads and restrictively filtered short-read unitigs, which are then reduced to a long-read overlap graph G. Instead of the more conventional approach of removing tips, bubbles, and other local features, LazyB stepwisely extracts subgraphs whose global properties approach a disjoint union of paths. First, a consistently oriented subgraph is extracted, which in a second step is reduced to a directed acyclic graph. In the next step, properties of proper interval graphs are used to extract contigs as maximum weight paths. These are translated into genomic sequences only in the final step. A prototype implementation of LazyB, entirely written in python, not only yields significantly more accurate assemblies of the yeast and fruit fly genomes compared to state-of-the-art pipelines but also requires much less computational effort. Our findings demonstrate a new low-cost method that enables the assembly of even large genomes with low computational effort.