| Title: | All generalized rose window graphs are hamiltonian |
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| Authors: | ID Bonvicini, Simona (Author)
ID Pisanski, Tomaž (Author)
ID Žitnik, Arjana (Author) |
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| Files: |  PDF - Presentation file, download (593,81 KB)
MD5: 98E3D3A248A223AF0F61CD5FC607131A
 URL - Source URL, visit https://link.springer.com/article/10.1007/s00373-026-03016-w
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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. |
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| Keywords: | Hamilton cycle, generalized rose window graphs, bicirculants, generalized Petersen graphs, Lovász conjecture |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.04.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | 20 str. |
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| Numbering: | Vol. 42, iss. 2, article no. 27 |
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| PID: | 20.500.12556/DiRROS-27826  |
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| UDC: | 519.17 |
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| ISSN on article: | 0911-0119 |
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| DOI: | 10.1007/s00373-026-03016-w |
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| COBISS.SI-ID: | 269644547 |
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| Note: |
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| Publication date in DiRROS: | 25.02.2026 |
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| Views: | 24 |
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| Downloads: | 9 |
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| Metadata: |    |
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