A note on sparseness conditions on chordless vertices of cycles

Conditions that disperse the chordless vertices of cycles correspond—sometimes in unexpected ways—to a variety of standard graph classes. Two examples: no cycle of length at least 5 has chordless vertices that are distance 2 apart in the cycle if and only if the graph is distance-hereditary; no cycle of length at least 5 has any chordless vertices if and only if every block of the graph is complete multipartite.