All generalized rose window graphs are hamiltonianBonvicini, Simona (Avtor) Pisanski, Tomaž (Avtor) Žitnik, Arjana (Avtor) Hamilton cyclegeneralized rose window graphsbicirculantsgeneralized Petersen graphsLovász conjectureA bicirculant is a regular, $d$-valent graph that admits a semiregular automorphism of order $m$ having two vertex-orbits of size $m$. The vertices of each orbit induce a circulant graph of order $m$ and the remaining edges span a regular bipartite graph of valence, say $s, 1 \le s \le d$, connecting the two vertex-orbits. Generalized Petersen graphs constitute a prominent family of bicirculants, with $d=3$ and $s=1$. In 1983, Brian Alspach proved that all generalized Petersen graphs are hamiltonian, except for the family $G(m, 2)$ with $m \equiv 5$ ($\mod 6$). In this paper we conjecture that among all connected bicirculants of valence at least $2$, there are no other exceptions. It follows from various sources that the conjecture is true for all cubic bicirculants. In this paper we prove the conjecture for quartic bicirulants with $s=2$, also known as the generalized rose window graphs.20262026-02-25 14:58:31Neznano27826UDK: 519.17ISSN pri članku: 0911-0119DOI: 10.1007/s00373-026-03016-wCOBISS_ID: 269644547sl