The elasticity of the DNA double helix varies with the underlying base pair sequence. This allows one to put mechanical cues into sequences that in turn influence the packaging of DNA into nucleosomes, DNA-wrapped protein cylinders. Nucleosomes dictate a broad range of biological processes, ranging from gene regulation, recombination, and replication to chromosome condensation. Here we map base pair sequences onto graphs and use shortest paths algorithms to determine which DNA stretches are easiest or hardest to bend inside a nucleosome. We further demonstrate how genetic and mechanical information can be multiplexed by studying paths through graphs of synonymous codons. Using this method we find that nucleosomes can be placed by mechanical cues nearly everywhere on the genome of baker's yeast (Saccharomyces cerevisiae).