The classical question raised by Lovász asks whether every Cayley graph is Hamiltonian. We present a short survey of various results in that direction and make some additional observations. In particular, we prove that every finite group G has a generating set of size at most log2 | G |, such that the corresponding Cayley graph contains a Hamiltonian cycle. We also present an explicit construction of 3-regular Hamiltonian expanders. © 2009 Elsevier B.V. All rights reserved.
Pak, I., & Radoičić, R. (2009). Hamiltonian paths in Cayley graphs. Discrete Mathematics, 309(17), 5501–5508. https://doi.org/10.1016/j.disc.2009.02.018