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Hamilton cycle and Hamilton path extendability of Cayley graphs on abelian groups
Miklavič, Štefko (Avtor), Šparl, Primož (Avtor)

URLURL - Predstavitvena datoteka, za dostop obiščite http://dx.doi.org/10.1002/jgt.20621 Povezava se odpre v novem oknu

Izvleček
In this paper the concepts of Hamilton cycle (HC) and Hamilton path (HP) extendability are introduced. A connected graph ▫$\Gamma$▫ is ▫$n$▫-HC-extendable if it contains a path of length ▫$n$▫ and if every such path is contained in some Hamilton cycle of ▫$\Gamma$▫. Similarly, ▫$\Gamma$▫ is weakly ▫$n$▫-HP-extendable if it contains a path of length ▫$n$▫ and if every such path is contained in some Hamilton path of ▫$\Gamma$▫. Moreover, ▫$\Gamma$▫ is strongly ▫$n$▫-HP-extendable if it contains a path of length ▫$n$▫ and if for every such path $P$ there is a Hamilton path of ▫$\Gamma$▫ starting with ▫$P$▫. These concepts are then studied for the class of connected Cayley graphs on abelian groups. It is proved that every connected Cayley graph on an abelian group of order at least three is 2-HC-extendable and a complete classification of 3-HC-extendable connected Cayley graphs of abelian groups is obtained. Moreover, it is proved that every connected Cayley graph on an abelian group of order at least five is weakly 4-HP-extendable.

Jezik:Angleški jezik
Ključne besede:graph theory, Hamilton cycle, Hamilton path, n-HC-extendable, strongly n-HP-extendable, weakly n-HP-extendable, Cayley graph, abelian group
Vrsta gradiva:Delo ni kategorizirano (r6)
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:PEF - Pedagoška fakulteta
Leto izida:2012
Št. strani:Str. 384-403
Številčenje:Vol. 70, no. 4
UDK:519.17
ISSN pri članku:0364-9024
DOI:10.1002/jgt.20621 Povezava se odpre v novem oknu
COBISS.SI-ID:1024359764 Povezava se odpre v novem oknu
Število ogledov:911
Število prenosov:220
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Gradivo je del revije

Naslov:Journal of graph theory
Skrajšan naslov:J. graph theory
Založnik:J. Wiley & Sons
ISSN:0364-9024
COBISS.SI-ID:25747712 Povezava se odpre v novem oknu

Sekundarni jezik

Jezik:Slovenski jezik
Ključne besede:teorija grafov, Hamiltonov cikel, Hamiltonova pot, Cayleyjev graf, Abelova grupa

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