Final answer:
The statement about linker histones aiding in the compaction of genomic DNA by influencing the DNA path after wrapping around the nucleosome core is true. The linker histones contribute to the higher-order structure of chromatin, which is essential for fitting the large amount of DNA within the cell nucleus.
Step-by-step explanation:
The linker histones indeed play a crucial role in compacting genomic DNA. The statement provided is true. Linker histones influence the path of the DNA after it has wrapped around the nucleosome core. In the process of DNA packaging, the first level involves the wrapping of DNA around an octamer of histone proteins to form a structure known as a nucleosome. This nucleosome arrangement, often described as "beads on a string," significantly reduces the length of DNA. The linker DNA connects individual nucleosomes. Subsequently, with the assistance of linker histones (a fifth histone variant), the nucleosome strings are further compacted into a higher-order structure, a 30-nm chromatin fiber, which then contributes to even further compaction of the chromosome.