| Naslov: | All generalized rose window graphs are hamiltonian |
|---|
| Avtorji: | ID Bonvicini, Simona (Avtor)
ID Pisanski, Tomaž (Avtor)
ID Žitnik, Arjana (Avtor) |
|---|
| Datoteke: |  PDF - Predstavitvena datoteka, prenos (593,81 KB)
MD5: 98E3D3A248A223AF0F61CD5FC607131A
 URL - Izvorni URL, za dostop obiščite https://link.springer.com/article/10.1007/s00373-026-03016-w
|
|---|
| Jezik: | Angleški jezik |
|---|
| Tipologija: | 1.01 - Izvirni znanstveni članek |
|---|
| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
|
|---|
| Povzetek: | 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. |
|---|
| Ključne besede: | Hamilton cycle, generalized rose window graphs, bicirculants, generalized Petersen graphs, Lovász conjecture |
|---|
| Status publikacije: | Objavljeno |
|---|
| Verzija 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/DiRROS-27826  |
|---|
| UDK: | 519.17 |
|---|
| ISSN pri članku: | 0911-0119 |
|---|
| DOI: | 10.1007/s00373-026-03016-w |
|---|
| COBISS.SI-ID: | 269644547 |
|---|
| Opomba: |
|
|---|
| Datum objave v DiRROS: | 25.02.2026 |
|---|
| Število ogledov: | 20 |
|---|
| Število prenosov: | 8 |
|---|
| Metapodatki: |    |
|---|
|
:
|
Kopiraj citat |
|---|
| | | | Objavi na: |  |
|---|
Postavite miškin kazalec na naslov za izpis povzetka. Klik na naslov izpiše
podrobnosti ali sproži prenos. |
