20.500.12556/DKUM-21991 HAMILTONSKE PRIZME HAMILTONIAN PRISMS Obstoja hamiltonske prizme v grafu leži med problemoma obstoja Hamiltonove poti in obstoja 2-sprehoda v grafu, kar v diplomskem delu podrobneje osvetlimo. Pri dokazovanju obstoja hamiltonskih prizem nad grafi si pomagamo s posebnim barvanjem povezav grafa. V prvem poglavju so opisane osnovne definicije in rezultati, povezani z grafi, prizmami in hamiltonskostjo. V drugem poglavju podrobneje obravnavamo prizme nad dvodelnimi grafi, kubičnimi grafi, posplošenimi Halinovimi grafi in grafi povezav ter predstavimo nekatere rezultate, ki se nanašajo na iskanje njihovih Hamiltonovih prizem. The diploma thesis examines the existence of Hamiltonian prisms over graphs. The problem of the existence of a Hamiltonian prism in a graph is directly related to the problems of the existence of a Hamiltonian path and of a 2-walk in a graph, which is analyzed in more detail in this work. In proving the existence of a Hamiltonian prism over a graph we use a special colouring of its edges. In the first chapter basic definitions and results related to graphs, prisms and hamiltonicity are described. In the second chapter we study in more detail the prisms over bipartite graphs, cubic graphs, generalized Halin graphs and line graphs, and present some results concerning the search for their Hamiltonian prisms. Teorija grafov prizma kartezični produkt Hamiltonov cikel Hamiltonov graf Hamiltonova prizma k-sprehod k-drevo k-faktor. Graph Theory prism cartesian product Hamilton cycle Hamiltonian graph Hamiltonian prism k-walk k-tree k-factor. true true false [Ž. Močivnik] Slovenski jezik Angleški jezik Diplomsko delo 2012-01-31 21:37:26 2012-02-27 14:32:56 2022-04-14 11:04:04 2023-12-27 03:32:36 2012 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 18944008 URN:SI:UM:DK:XILOUBO9 UNI_Mocivnik_Zan_2012.pdf UNI_Mocivnik_Zan_2012.pdf 1 9345E6F88BFC8561EF5DC3B0260A5424 4e8a0c88ec1a609b5b9b7b2ba0b43b4a74b96177b735d048430c30869f08eb7a 61fae764-7c06-11eb-bb7a-00155d0001ca 20.500.12556/dkum/8ecc3b73-8b18-4a0d-bd78-f9d69bf16762 https://dk.um.si/Dokument.php?lang=slv&id=28191 Fakulteta za naravoslovje in matematiko 0 0 0