All generalized rose window graphs are hamiltonian

Bonvicini, Simona (avtor), Pisanski, Tomaž (avtor), Žitnik, Arjana (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: Hamilton cycle, generalized rose window graphs, bicirculants, generalized Petersen graphs, Lovász conjecture
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.04.2026
• Leto izida: 2026
• Št. strani: 20 str.
• Številčenje: Vol. 42, iss. 2, article no. 27
• PID: 20.500.12556/RUL-179843
• UDK: 519.17
• ISSN pri članku: 0911-0119
• DOI: 10.1007/s00373-026-03016-w
• COBISS.SI-ID: 269644547
• Datum objave v RUL: 25.02.2026

Gradivo je del revije

• Naslov: Graphs and combinatorics
• Skrajšan naslov: Graphs comb.
• Založnik: Springer Nature
• ISSN: 0911-0119
• COBISS.SI-ID: 25536512

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: Hamiltonov cikel, posplošeni rozetni grafi, bicirkulanti, posplošeni Petersenovi grafi, Lovászova domneva