The practical use of graph-based reference genomes depends on the ability to align reads to them. Performing substring queries to paths through these graphs lies at the core of this task. The combination of increasing pattern length and encoded variations inevitably leads to a combinatorial explosion of the search space. Instead of heuristic filtering or pruning steps to reduce the complexity, we propose CHOP, a method that constrains the search space by exploiting haplotype information, bounding the search space to the number of haplotypes so that a combinatorial explosion is prevented. We show that CHOP can be applied to large and complex datasets, by applying it on a graph-based representation of the human genome encoding all 80 million variants reported by the 1000 Genomes Project.