Background: Long-read sequencing technologies are the ultimate solution for genome repeats, allowing near reference-level reconstructions of large genomes. However, long-read de novo assembly pipelines are computationally intense and require a considerable amount of coverage, thereby hindering their broad application to the assembly of large genomes. Alternatively, hybrid assembly methods that combine short-and long-read sequencing technologies can reduce the time and cost required to produce de novo assemblies of large genomes. Results: Here, we propose a new method, called Fast-SG, that uses a new ultrafast alignment-free algorithm specifically designed for constructing a scaffolding graph using lightweight data structures. Fast-SG can construct the graph from either short or long reads. This allows the reuse of efficient algorithms designed for short-read data and permits the definition of novel modular hybrid assembly pipelines. Using comprehensive standard datasets and benchmarks, we show how Fast-SG outperforms the state-of-the-art short-read aligners when building the scaffolding graph and can be used to extract linking information from either raw or error-corrected long reads. We also show how a hybrid assembly approach using Fast-SG with shallow long-read coverage (5X) and moderate computational resources can produce long-range and accurate reconstructions of the genomes of Arabidopsis thaliana (Ler-0) and human (NA12878). Conclusions: Fast-SG opens a door to achieve accurate hybrid long-range reconstructions of large genomes with low effort, high portability, and low cost.