20.500.12556/DKUM-86505 Counting Hamiltonian cycles in 2-tiled graphs 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. crossing number crossing-critical graph Hamiltonian cycle križno število križno kritični graf Hamiltonov cikel true true true Angleški jezik Slovenski jezik Znanstveno delo 2023-12-06 08:02:00 2023-12-21 08:16:53 2025-02-28 10:12:28 0000-00-00 00:00:00 2021 0 0 str. 1-27 št. 6 Letn. 9 2021 0000-00-00 Zaloznikova Objavljeno apc 2021-01-29 2021-03-16 2021-03-23 519.17 61574403 10.3390/math9060693 2227-7390 mathematics-09-00693-2.pdf mathematics-09-00693-2.pdf 1 F6774F433E0B804008E2B179391F259C 45df8b8af9e43c5d92860db42dfe06bb33b7567e95c52ddf804e474e68c5d3f0 b1fdc4eb-9405-11ee-8142-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=174659 https://www.mdpi.com/2227-7390/9/6/693 1 a50dc897-9405-11ee-8142-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=174658 Fakulteta za naravoslovje in matematiko 0 0 0