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Statements

Subject Item
n2:RIV%2F49777513%3A23520%2F09%3A00501873%21RIV10-MSM-23520___
rdf:type
n14:Vysledek skos:Concept
dcterms:description
A cycle that contains every vertex of a graph is called a hamiltonian cycle and a graph which contains a hamiltonian cycle is called a hamiltonian graph. The problem of the existence of a hamiltonian cycle is closely related to the well known problem of a travelling salesman. These problems are NP-complete and NP-hard, respectively. While some necessary and sufficient conditions are known, to date, no practical characterization of hamiltonian graphs has been found. There are several ways to generalize the notion of a hamiltonian cycle. In this thesis we make original contributions in two of them, namely, k-walks and r-trestles. In particular, as our main results, we present several new sufficient conditions for the existence of k-walks and r-trestles in a graph. Furthermore we present results dealing with recognizing graphs with an r-trestle and finding them in K_{1;r}-free graphs. A cycle that contains every vertex of a graph is called a hamiltonian cycle and a graph which contains a hamiltonian cycle is called a hamiltonian graph. The problem of the existence of a hamiltonian cycle is closely related to the well known problem of a travelling salesman. These problems are NP-complete and NP-hard, respectively. While some necessary and sufficient conditions are known, to date, no practical characterization of hamiltonian graphs has been found. There are several ways to generalize the notion of a hamiltonian cycle. In this thesis we make original contributions in two of them, namely, k-walks and r-trestles. In particular, as our main results, we present several new sufficient conditions for the existence of k-walks and r-trestles in a graph. Furthermore we present results dealing with recognizing graphs with an r-trestle and finding them in K_{1;r}-free graphs.
dcterms:title
Factors and cycles in graphs Factors and cycles in graphs
skos:prefLabel
Factors and cycles in graphs Factors and cycles in graphs
skos:notation
RIV/49777513:23520/09:00501873!RIV10-MSM-23520___
n3:aktivita
n11:P
n3:aktivity
P(1M0545)
n3:dodaniDat
n10:2010
n3:domaciTvurceVysledku
n12:3975746
n3:druhVysledku
n16:O
n3:duvernostUdaju
n4:S
n3:entitaPredkladatele
n6:predkladatel
n3:idSjednocenehoVysledku
314561
n3:idVysledku
RIV/49777513:23520/09:00501873
n3:jazykVysledku
n5:eng
n3:klicovaSlova
hamiltonian cycle; walks; trestles
n3:klicoveSlovo
n8:trestles n8:hamiltonian%20cycle n8:walks
n3:kontrolniKodProRIV
[92DBB5736BAE]
n3:obor
n15:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
1
n3:projekt
n17:1M0545
n3:rokUplatneniVysledku
n10:2009
n3:tvurceVysledku
Teska, Jakub
n9:organizacniJednotka
23520