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1.
Hamilton cycle and Hamilton path extendability of Cayley graphs on abelian groups
Štefko Miklavič, Primož Šparl, 2012, original scientific article

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.
Found in: ključnih besedah
Summary of found: ......
Keywords: graph theory, Hamilton cycle, Hamilton path, n-HC-extendable, strongly n-HP-extendable, weakly n-HP-extendable, Cayley graph, abelian group
Published: 15.10.2013; Views: 1285; Downloads: 78
URL Full text (0,00 KB)

2.
Equistarable bipartite graphs
Martin Milanič, Endre Boros, Nina Chiarelli, 2015, original scientific article

Found in: ključnih besedah
Summary of found: ......
Keywords: equistable graph, general partition graph, bipartite graph, equistarable graph, 2-extendable graph
Published: 03.04.2017; Views: 883; Downloads: 97
URL Full text (0,00 KB)

3.
On the extendability of quasi-strongly regular graphs with diameter 2
Hermina Alajbegović, Almir Huskanović, Štefko Miklavič, Primož Šparl, 2018, original scientific article

Found in: ključnih besedah
Summary of found: ......
Keywords: regular graph, quasi-strongly regular graph, diameter 2, l-extendable
Published: 08.06.2018; Views: 487; Downloads: 78
URL Full text (0,00 KB)

4.
The classification of 2-extendable edge-regular graphs with diameter 2
Klavdija Kutnar, Dragan Marušič, Štefko Miklavič, Primož Šparl, 2019, original scientific article

Found in: ključnih besedah
Summary of found: Zadetek v naslovu
Keywords: edge-regular, diameter, 2-extendable
Published: 13.02.2019; Views: 212; Downloads: 14
URL Full text (0,00 KB)

5.
Matching extensions in regular graphs with small diameter
Ivana Koroman, 2019, master's thesis

Found in: ključnih besedah
Summary of found: ......
Keywords: l-extendable, l 1/2-extendable, regular graph, edge-regular graph, strongly regular graph, diameter 2, diameter 3
Published: 25.07.2019; Views: 254; Downloads: 2
URL Full text (0,00 KB)

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