Erdős-Gyárfás conjecture for some families of Cayley graphs.

The Paul Erdős and András Gyárfás conjecture states that every graph of minimum degree at least 3 contains a simple cycle whose length is a power of two. In this paper, we prove that the conjecture holds for Cayley graphs on generalized quaternion groups, dihedral groups, semidihedral groups and groups of order $$p^3$$ . [ABSTRACT FROM AUTHOR]