Final answer:
Linker histones aid in DNA compaction by affecting the arrangement of DNA after it wraps around nucleosome cores, making the statement true.
Step-by-step explanation:
Linker histones indeed have a crucial role in the compaction of genomic DNA. They influence the structure of chromatin by contributing to the formation of the 30-nm chromatin fiber, which is a more compact version of the beads on a string structure. This is achieved after DNA wraps around nucleosomes, which are composed of a core of eight histone proteins. Linker histones bind to the linker DNA, which is the DNA connecting nucleosomes, to help coil the nucleosomes and linker DNA into this dense fiber. Therefore, the statement that linker histones help compact genomic DNA by influencing the path of DNA after it has wrapped around the nucleosome core is true.