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Hamilton cycle and Hamilton path extendability of Cayley graphs on abelian groups
ID
Miklavič, Štefko
(
Author
),
ID
Šparl, Primož
(
Author
)
URL  Presentation file, Visit
http://dx.doi.org/10.1002/jgt.20621
Abstract
In this paper the concepts of Hamilton cycle (HC) and Hamilton path (HP) extendability are introduced. A connected graph ▫$\Gamma$▫ is ▫$n$▫HCextendable 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 ▫$n$▫HPextendable 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 ▫$n$▫HPextendable 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 2HCextendable and a complete classification of 3HCextendable 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 4HPextendable.
Language:
English
Keywords:
graph theory
,
Hamilton cycle
,
Hamilton path
,
nHCextendable
,
strongly nHPextendable
,
weakly nHPextendable
,
Cayley graph
,
abelian group
Work type:
Not categorized
Typology:
1.01  Original Scientific Article
Organization:
PEF  Faculty of Education
Year:
2012
Number of pages:
Str. 384403
Numbering:
Vol. 70, no. 4
PID:
20.500.12556/RUL84783
UDC:
519.17
ISSN on article:
03649024
DOI:
10.1002/jgt.20621
COBISS.SIID:
1024359764
Publication date in RUL:
09.09.2016
Views:
1270
Downloads:
245
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Record is a part of a journal
Title:
Journal of graph theory
Shortened title:
J. graph theory
Publisher:
J. Wiley & Sons
ISSN:
03649024
COBISS.SIID:
25747712
Secondary language
Language:
Slovenian
Keywords:
teorija grafov
,
Hamiltonov cikel
,
Hamiltonova pot
,
Cayleyjev graf
,
Abelova grupa
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