| Title: | Counting Hamiltonian cycles in 2-tiled graphs |
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| Authors: | ID Vegi Kalamar, Alen (Author)
ID Žerak, Tadej (Author)
ID Bokal, Drago (Author) |
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| Files: |  mathematics-09-00693-2.pdf (424,22 KB)
MD5: F6774F433E0B804008E2B179391F259C
 https://www.mdpi.com/2227-7390/9/6/693
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| Language: | English |
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| Work type: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | 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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| Keywords: | crossing number, crossing-critical graph, Hamiltonian cycle |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 29.01.2021 |
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| Article acceptance date: | 16.03.2021 |
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| Publication date: | 23.03.2021 |
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| Year of publishing: | 2021 |
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| Number of pages: | str. 1-27 |
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| Numbering: | Letn. 9, št. 6 |
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| PID: | 20.500.12556/DKUM-86505  |
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| UDC: | 519.17 |
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| ISSN on article: | 2227-7390 |
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| COBISS.SI-ID: | 61574403 |
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| DOI: | 10.3390/math9060693 |
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| Publication date in DKUM: | 21.12.2023 |
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| Views: | 661 |
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| Downloads: | 621 |
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| Metadata: |    |
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| Categories: | Misc.
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