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Title:
HAMILTONSKE PRIZME
Authors:
ID
Močivnik, Žan
(Author)
ID
Brešar, Boštjan
(Mentor)
More about this mentor...
Files:
UNI_Mocivnik_Zan_2012.pdf
(2,17 MB)
MD5: 9345E6F88BFC8561EF5DC3B0260A5424
PID:
20.500.12556/dkum/8ecc3b73-8b18-4a0d-bd78-f9d69bf16762
Language:
Slovenian
Work type:
Undergraduate thesis
Organization:
FNM - Faculty of Natural Sciences and Mathematics
Abstract:
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.
Keywords:
Teorija grafov
,
prizma
,
kartezični produkt
,
Hamiltonov cikel
,
Hamiltonov graf
,
Hamiltonova prizma
,
k-sprehod
,
k-drevo
,
k-faktor.
Place of publishing:
Maribor
Publisher:
[Ž. Močivnik]
Year of publishing:
2012
PID:
20.500.12556/DKUM-21991
UDC:
51(043.2)
COBISS.SI-ID:
18944008
NUK URN:
URN:SI:UM:DK:XILOUBO9
Publication date in DKUM:
27.02.2012
Views:
3308
Downloads:
291
Metadata:
Categories:
FNM
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:
MOČIVNIK, Žan, 2012,
HAMILTONSKE PRIZME
[online]. Bachelor’s thesis. Maribor : Ž. Močivnik. [Accessed 18 March 2025]. Retrieved from: https://dk.um.si/IzpisGradiva.php?lang=eng&id=21991
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Secondary language
Language:
English
Title:
HAMILTONIAN PRISMS
Abstract:
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.
Keywords:
Graph Theory
,
prism
,
cartesian product
,
Hamilton cycle
,
Hamiltonian graph
,
Hamiltonian prism
,
k-walk
,
k-tree
,
k-factor.
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