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1.
Hamilton paths in vertex-transitive graphs of order 10p
Klavdija Kutnar, Dragan Marušič, Cui Zhang, 2012, izvirni znanstveni članek

Opis: It is shown that every connected vertex-transitive graph of order ▫$10p$▫, ▫$p \ne 7$▫ a prime, which is not isomorphic to a quasiprimitive graph arising from the action of PSL▫$(2,k)$▫ on cosets of ▫$\mathbb{Z}_k \times \mathbb{Z}_{(k-1)/10}$▫, contains a Hamilton path.
Najdeno v: ključnih besedah
Povzetek najdenega: ...graph, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group...
Ključne besede: graph, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1637; Prenosov: 11
URL Polno besedilo (0,00 KB)

2.
Hamiltonicity of vertex-transitive graphs of order 4p
Klavdija Kutnar, Dragan Marušič, 2008, izvirni znanstveni članek

Opis: It is shown that every connected vertex-transitive graph of order ▫$4p$▫, where ▫$p$▫ is a prime, is hamiltonian with the exception of the Coxeter graph which is known to possess a Hamilton path.
Najdeno v: ključnih besedah
Povzetek najdenega: ...▫$4p$▫, where ▫$p$▫ is a prime, is hamiltonian with the exception of the Coxeter graph... ...graph theory, vertex-transitive graphs, Hamilton cycle, automorphism group...
Ključne besede: graph theory, vertex-transitive graphs, Hamilton cycle, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1524; Prenosov: 17
URL Polno besedilo (0,00 KB)

3.
Hamiltonicity of cubic Cayley graphs
Dragan Marušič, Henry Glover, Klavdija Kutnar, Aleksander Malnič, 2012, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Najdeno v: ključnih besedah
Povzetek najdenega: ...Cayley graph, Hamilton path, Hamilton cycle, arc-transitive graph, Cayley map,...
Ključne besede: Cayley graph, Hamilton path, Hamilton cycle, arc-transitive graph, Cayley map
Objavljeno: 15.10.2013; Ogledov: 1309; Prenosov: 21
URL Polno besedilo (0,00 KB)

4.
Construction of Hamilton cycles in (2,s,3)-Cayley graphs
Klavdija Kutnar, 2010, objavljeni povzetek znanstvenega prispevka na konferenci

Najdeno v: ključnih besedah
Povzetek najdenega: ...Hamilton cycle, Cayley graph, ...
Ključne besede: Hamilton cycle, Cayley graph
Objavljeno: 15.10.2013; Ogledov: 1258; Prenosov: 8
URL Polno besedilo (0,00 KB)

5.
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.
Najdeno v: ključnih besedah
Ključne besede: graph theory, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1586; Prenosov: 14
URL Polno besedilo (0,00 KB)

6.
On Hamiltonicity of circulant digraphs of outdegree three
Štefko Miklavič, Primož Šparl, 2009, izvirni znanstveni članek

Opis: This paper deals with Hamiltonicity of connected loopless circulant digraphs of outdegree three with connection set of the form ▫$\{a,ka,c\}$▫, where ▫$k$▫ is an integer. In particular, we prove that if ▫$k=-1$▫ or ▫$k=2$▫ such a circulant digraph is Hamiltonian if and only if it is not isomorphic to the circulant digraph on 12 vertices with connection set ▫$\{3,6,4\}$▫.
Najdeno v: ključnih besedah
Povzetek najdenega: ...graph theory, circulant digraph, Hamilton cycle...
Ključne besede: graph theory, circulant digraph, Hamilton cycle
Objavljeno: 15.10.2013; Ogledov: 1221; Prenosov: 38
URL Polno besedilo (0,00 KB)

7.
Hamilton cycles in (2, odd, 3)-Cayley graphs
Henry Glover, Klavdija Kutnar, Aleksander Malnič, Dragan Marušič, 2012, izvirni znanstveni članek

Opis: In 1969, Lovász asked if every finite, connected vertex-transitive graph has a Hamilton path. In spite of its easy formulation, no major breakthrough has been achieved thus far, and the problem is now commonly accepted to be very hard. The same holds for the special subclass of Cayley graphs where the existence of Hamilton cycles has been conjectured. In 2007, Glover and Marušič proved that a cubic Cayley graph on a finite ▫$(2, s, 3)$▫-generated group ▫$G = \langle a, x| a^2 = x^s = (ax)^3 = 1, \dots \rangle$▫ has a Hamilton path when ▫$|G|$▫ is congruent to 0 modulo 4, and has a Hamilton cycle when ▫$|G|$▫ is congruent to 2 modulo 4. The Hamilton cycle was constructed, combining the theory of Cayley maps with classical results on cyclic stability in cubic graphs, as the contractible boundary of a tree of faces in the corresponding Cayley map. With a generalization of these methods, Glover, Kutnar and Marušič in 2009 resolved the case when, apart from ▫$|G|$▫, also ▫$s$▫ is congruent to 0 modulo 4. In this article, with a further extension of the above "tree of faces" approach, a Hamilton cycle is shown to exist whenever ▫$|G|$▫ is congruent to 0 modulo 4 and s is odd. This leaves ▫$|G|$▫ congruent to 0 modulo 4 with s congruent to 2 modulo 4 as the only remaining open case. In this last case, however, the "tree of faces" approach cannot be applied, and so entirely different techniques will have to be introduced if one is to complete the proof of the existence of Hamilton cycles in cubic Cayley graphs arising from finite ▫$(2, s, 3)$▫-generated groups.
Najdeno v: ključnih besedah
Povzetek najdenega: ...Cayley graphs where the existence of Hamilton cycles has been conjectured. In 2007, Glover and...
Ključne besede: Cayley graph, Hamilton cycle, arc-transitive graph, 1-regular action, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1173; Prenosov: 47
URL Polno besedilo (0,00 KB)

8.
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.
Najdeno v: ključnih besedah
Ključne besede: graph theory, Hamilton cycle, Hamilton path, n-HC-extendable, strongly n-HP-extendable, weakly n-HP-extendable, Cayley graph, abelian group
Objavljeno: 15.10.2013; Ogledov: 1189; Prenosov: 60
URL Polno besedilo (0,00 KB)

9.
Special issue of discrete mathematics on Hamiltonicity problem for vertex-transitive (Cayley) graphs
Dragan Marušič, 2009, predgovor, spremna beseda

Najdeno v: ključnih besedah
Povzetek najdenega: ... Hamilton cycle, Hamilton path, Vetrex-transitive graph, Cayley graph,...
Ključne besede: Hamilton cycle, Hamilton path, Vetrex-transitive graph, Cayley graph
Objavljeno: 15.10.2013; Ogledov: 1263; Prenosov: 13
URL Polno besedilo (0,00 KB)

10.
On cyclic edge-connectivity of fullerenes
Dragan Marušič, Klavdija Kutnar, 2008, izvirni znanstveni članek

Opis: A graph is said to be cyclically ▫$k$▫-edge-connected, if at least ▫$k$▫ edges must be removed to disconnect it into two components, each containing a cycle. Such a set of ▫$k$▫ edges is called a cyclic-k-edge cutset and it is called a trivial cyclic-k-edge cutset if at least one of the resulting two components induces a single ▫$k$▫-cycle. It is known that fullerenes, that is, 3-connected cubic planar graphs all of whose faces are pentagons and hexagons, are cyclically 5-edge-connected. In this article it is shown that a fullerene ▫$F$▫ containing a nontrivial cyclic-5-edge cutset admits two antipodal pentacaps, that is, two antipodal pentagonal faces whose neighboring faces are also pentagonal. Moreover, it is shown that ▫$F$▫ has a Hamilton cycle, and as a consequence at least ▫$15 \cdot 2^{n/20-1/2}$▫ perfect matchings, where ▫$n$▫ is the order of ▫$F$▫.
Najdeno v: ključnih besedah
Povzetek najdenega: ...it is shown that ▫$F$▫ has a Hamilton cycle, and as a consequence at least... ...it into two components, each containing a cycle. Such a set of ▫$k$▫ edges is...
Ključne besede: graph, fullerene graph, cyclic edge-connectivity, hamilton cycle, perfect matching
Objavljeno: 03.04.2017; Ogledov: 608; Prenosov: 58
URL Polno besedilo (0,00 KB)

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