| Naslov: | Counting Hamiltonian cycles in 2-tiled graphs |
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| Avtorji: | ID Vegi Kalamar, Alen (Avtor)
ID Žerak, Tadej (Avtor)
ID Bokal, Drago (Avtor) |
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| Datoteke: |  mathematics-09-00693-2.pdf (424,22 KB)
MD5: F6774F433E0B804008E2B179391F259C
 https://www.mdpi.com/2227-7390/9/6/693
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| Jezik: | Angleški jezik |
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| Vrsta gradiva: | Znanstveno delo |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: | FNM - Fakulteta za naravoslovje in matematiko
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| Opis: | In 1930, Kuratowski showed that �3,3 and �5 are the only two minor-minimal nonplanar graphs. Robertson and Seymour extended finiteness of the set of forbidden minors for any surface. Širáň and Kochol showed that there are infinitely many k-crossing-critical graphs for any �≥2, even if restricted to simple 3-connected graphs. Recently, 2-crossing-critical graphs have been completely characterized by Bokal, Oporowski, Richter, and Salazar. We present a simplified description of large 2-crossing-critical graphs and use this simplification to count Hamiltonian cycles in such graphs. We generalize this approach to an algorithm counting Hamiltonian cycles in all 2-tiled graphs, thus extending the results of Bodroža-Pantić, Kwong, Doroslovački, and Pantić. |
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| Ključne besede: | crossing number, crossing-critical graph, Hamiltonian cycle |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Poslano v recenzijo: | 29.01.2021 |
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| Datum sprejetja članka: | 16.03.2021 |
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| Datum objave: | 23.03.2021 |
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| Leto izida: | 2021 |
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| Št. strani: | str. 1-27 |
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| Številčenje: | Letn. 9, št. 6 |
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| PID: | 20.500.12556/DKUM-86505  |
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| UDK: | 519.17 |
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| COBISS.SI-ID: | 61574403 |
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| DOI: | 10.3390/math9060693 |
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| ISSN pri članku: | 2227-7390 |
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| Datum objave v DKUM: | 21.12.2023 |
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| Število ogledov: | 662 |
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| Število prenosov: | 621 |
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| Metapodatki: |    |
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| Področja: | Ostalo
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