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

Miklavič, Štefko (author), Šparl, Primož (author)

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.

• Language: English
• Keywords: graph theory, Hamilton cycle, Hamilton path, n-HC-extendable, strongly n-HP-extendable, weakly n-HP-extendable, 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. 384-403
• Numbering: Vol. 70, no. 4
• PID: 20.500.12556/RUL-84783
• UDC: 519.17
• ISSN on article: 0364-9024
• DOI: 10.1002/jgt.20621
• COBISS.SI-ID: 1024359764
• Publication date in RUL: 09.09.2016

Record is a part of a journal

• Title: Journal of graph theory
• Shortened title: J. graph theory
• Publisher: J. Wiley & Sons
• ISSN: 0364-9024
• COBISS.SI-ID: 25747712

Secondary language

• Language: Slovenian
• Keywords: teorija grafov, Hamiltonov cikel, Hamiltonova pot, Cayleyjev graf, Abelova grupa