Hamilton cycle and Hamilton path extendability of Cayley graphs on abelian groups

Miklavič, Štefko; Šparl, Primož

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Title:	Hamilton cycle and Hamilton path extendability of Cayley graphs on abelian groups
Authors:	ID Miklavič, Štefko (Author) ID Šparl, Primož (Author)
Files:	http://dx.doi.org/10.1002/jgt.20621
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	IAM - Andrej Marušič Institute
Abstract:	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.
Keywords:	graph theory, Hamilton cycle, Hamilton path, n-HC-extendable, strongly n-HP-extendable, weakly n-HP-extendable, Cayley graph, abelian group
Year of publishing:	2012
Number of pages:	str. 384-403
Numbering:	Vol. 70, no. 4
PID:	20.500.12556/RUP-3539
ISSN:	0364-9024
UDC:	519.17
COBISS.SI-ID:	1024359764
Publication date in RUP:	15.10.2013
Views:	2821
Downloads:	143
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