20.500.12556/DiRROS-27826 All generalized rose window graphs are hamiltonian A 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. Hamilton cycle generalized rose window graphs bicirculants generalized Petersen graphs Lovász conjecture Hamiltonov cikel posplošeni rozetni grafi bicirkulanti posplošeni Petersenovi grafi Lovászova domneva true false true Angleški jezik Slovenski jezik Neznano 2026-02-25 14:58:31 2026-02-25 14:58:31 2026-02-26 03:55:16 0000-00-00 00:00:00 2026 0 0 20 str. iss. 2, article no. 27 Vol. 42 Apr. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-04-01 519.17 0911-0119 10.1007/s00373-026-03016-w 269644547 s00373-026-03016-w.pdf s00373-026-03016-w.pdf 1 98E3D3A248A223AF0F61CD5FC607131A 22ab4bac0eb1f8e5380b3d8d74e5d3974c790d5be322e49607c5be48c788a4ba 81d9333e-1252-11f1-9cb0-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=40917 https://link.springer.com/article/10.1007/s00373-026-03016-w 1 138f411d-1252-11f1-9cb0-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=40915 Inštitut za matematiko, fiziko in mehaniko 0 0 0