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The price of connectivity for cycle transversals
Tatiana Romina Hartinger, Matthew Johnson, Martin Milanič, Daniël Paulusma, 2015, objavljeni znanstveni prispevek na konferenci

Ključne besede: price of connectivity, hereditary graph class, path, cycle, transversal
Objavljeno v RUP: 08.08.2016; Ogledov: 2802; Prenosov: 121
URL Povezava na celotno besedilo

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Hamilton cycle and Hamilton path extendability of Cayley graphs on abelian groups
Štefko Miklavič, Primož Šparl, 2012, izvirni znanstveni članek

Opis: 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.
Ključne besede: graph theory, Hamilton cycle, Hamilton path, n-HC-extendable, strongly n-HP-extendable, weakly n-HP-extendable, Cayley graph, abelian group
Objavljeno v RUP: 15.10.2013; Ogledov: 2726; Prenosov: 143
URL Povezava na celotno besedilo

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Hamilton paths and cycles in vertex-transitive graphs of order 6p
Klavdija Kutnar, Primož Šparl, 2009, izvirni znanstveni članek

Opis: It is shown that every connected vertex-transitive graph of order ▫$6p$▫, where ▫$p$▫ is a prime, contains a Hamilton path. Moreover, it is shown that, except for the truncation of the Petersen graph, every connected vertex-transitive graph of order ▫$6p$▫ which is not genuinely imprimitive contains a Hamilton cycle.
Ključne besede: graph theory, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group
Objavljeno v RUP: 15.10.2013; Ogledov: 3340; Prenosov: 40
URL Povezava na celotno besedilo

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Recent trends and future directions in vertex-transitive graphs
Klavdija Kutnar, Dragan Marušič, 2008, izvirni znanstveni članek

Opis: A graph is said to be vertex-transitive if its automorphism group acts transitively on the vertex set. Some recent developments and possible future directions regarding two famous open problems, asking about existence of Hamilton paths and existence of semiregular automorphisms in vertex-transitive graphs, are discussed, together with some recent results on arc-transitive graphs and half-arc-transitive graphs, two special classes of vertex-transitive graphs that have received particular attention over the last decade.
Ključne besede: vertex-transitive graph, arc-transitive graph, half-arc-transitive graph, Hamilton cycle, Hamilton path, semiregular group, (im)primitive group
Objavljeno v RUP: 15.10.2013; Ogledov: 3050; Prenosov: 131
.pdf Celotno besedilo (183,49 KB)

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