Naslov: Hamilton cycle and Hamilton path extendability of Cayley graphs on abelian groups Miklavič, Štefko (Avtor)Šparl, Primož (Avtor) http://dx.doi.org/10.1002/jgt.20621 Angleški jezik Delo ni kategorizirano 1.01 - Izvirni znanstveni članek IAM - Inštitut Andrej Marušič 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. graph theory, Hamilton cycle, Hamilton path, n-HC-extendable, strongly n-HP-extendable, weakly n-HP-extendable, Cayley graph, abelian group 2012 str. 384-403 Vol. 70, no. 4 0364-9024 519.17 1024359764 1224 70 Gradivo ni uvrščeno v področja.

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## Sekundarni jezik

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

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