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

 URL - Predstavitvena datoteka, za dostop obiščite http://dx.doi.org/10.1002/jgt.20621

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 graph theory, Hamilton cycle, Hamilton path, n-HC-extendable, strongly n-HP-extendable, weakly n-HP-extendable, Cayley graph, abelian group Delo ni kategorizirano (r6) 1.01 - Izvirni znanstveni članek PEF - Pedagoška fakulteta 2012 Str. 384-403 Vol. 70, no. 4 519.17 0364-9024 10.1002/jgt.20621 1024359764 911 220 (0 glasov) Ocenjevanje je dovoljeno samo prijavljenim uporabnikom. AddThis uporablja piškotke, za katere potrebujemo vaše privoljenje.Uredi privoljenje...

Naslov: Journal of graph theory J. graph theory J. Wiley & Sons 0364-9024 25747712

## Sekundarni jezik

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

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