Counting Hamiltonian cycles in 2-tiled graphsVegi Kalamar, Alen (Avtor) Žerak, Tadej (Avtor) Bokal, Drago (Avtor) crossing numbercrossing-critical graphHamiltonian cycleIn 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.20212023-12-06 08:02:00Znanstveno delo86505UDK: 519.17COBISS_ID: 61574403DOI: 10.3390/math9060693ISSN pri članku: 2227-7390sl