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2. A novel characterization of cubic Hamiltonian graphs via the associated quartic graphsSimona Bonvicini, Tomaž Pisanski, 2017, original scientific article Abstract: We give a necessary and sufficient condition for a cubic graph to be Hamiltonian by analyzing Eulerian tours in certain spanning subgraphs of the quartic graph associated with the cubic graph by 1-factor contraction. This correspondence is most useful in the case when it induces a blue and red 2-factorization of the associated quartic graph. We use this condition to characterize the Hamiltonian ▫$I$▫-graphs, a further generalization of generalized Petersen graphs. The characterization of Hamiltonian ▫$I$▫-graphs follows from the fact that one can choose a 1-factor in any ▫$I$▫-graph in such a way that the corresponding associated quartic graph is a graph bundle having a cycle graph as base graph and a fiber and the fundamental factorization of graph bundles playing the role of blue and red factorization. The techniques that we develop allow us to represent Cayley multigraphs of degree 4, that are associated to abelian groups, as graph bundles. Moreover, we can find a family of connected cubic (multi)graphs that contains the family of connected ▫$I$▫-graphs as a subfamily. Keywords: generalized Petersen graphs, I-graphs, Hamiltonian cycles, Eulerian tours, Cayley multigraphs Published in RUP: 03.01.2022; Views: 814; Downloads: 16 Full text (1,01 MB) |
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6. Hitro prepoznavanje nekaterih parametričnih grafovskih družin : magistrsko deloNina Klobas, 2020, master's thesis Keywords: posplošeni Petersenovi grafi, I-grafi, dvojno posplošeni Petersenovi grafi, zložene kocke, algoritem prepoznavanja grafov, ciklična regularnost, generalized Petersen graphs, I-graphs, double generalized Peteren graphs, folded cubes, recognition algorithm, cycle regularity Published in RUP: 02.10.2020; Views: 1462; Downloads: 17 Link to full text |
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10. Predicting the success of an invader : niche shift versus niche conservatismStéphanie Sherpa, Maya Guéguen, Julien Renaud, Michael G. B. Blum, Thierry Gaude, Frédéric Laporte, Mustafa Akiner, Bulent Alten, Carles Aranda, Katja Kalan, 2019, original scientific article Keywords: Aedes albopistus, ecological niche modeling, generalized dissimilarity modeling, genotype- environment association, geometric morphometrics, niche conservatism, RAD sequencing, rapid adaptation Published in RUP: 11.02.2020; Views: 1427; Downloads: 135 Link to full text This document has more files! More... |