1. Hamilton paths in vertex-transitive graphs of order 10pKlavdija Kutnar, Dragan Marušič, Cui Zhang, 2012, original scientific article Abstract: 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. Found in: ključnih besedah Keywords: graph, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group Published: 15.10.2013; Views: 1688; Downloads: 11 Full text (0,00 KB) |
2. Hamiltonicity of cubic Cayley graphsDragan Marušič, Henry Glover, Klavdija Kutnar, Aleksander Malnič, 2012, published scientific conference contribution abstract (invited lecture) Found in: ključnih besedah Summary of found: ...Cayley graph, Hamilton path, Hamilton cycle, arc-transitive graph, Cayley map,... Keywords: Cayley graph, Hamilton path, Hamilton cycle, arc-transitive graph, Cayley map Published: 15.10.2013; Views: 1358; Downloads: 24 Full text (0,00 KB) |
3. Hamilton paths and cycles in vertex-transitive graphs of order 6pKlavdija Kutnar, Primož Šparl, 2009, original scientific article Abstract: 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. Found in: ključnih besedah Summary of found: ...▫$p$▫ is a prime, contains a Hamilton path. Moreover, it is shown that, except for... Keywords: graph theory, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group Published: 15.10.2013; Views: 1624; Downloads: 14 Full text (0,00 KB) |
4. Hamilton cycle and Hamilton path extendability of Cayley graphs on abelian groupsŠtefko 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 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: 1219; Downloads: 69 Full text (0,00 KB) |
5. Special issue of discrete mathematics on Hamiltonicity problem for vertex-transitive (Cayley) graphsDragan Marušič, 2009, preface, afterword Found in: ključnih besedah Summary of found: ... Hamilton cycle, Hamilton path, Vetrex-transitive graph, Cayley graph,... Keywords: Hamilton cycle, Hamilton path, Vetrex-transitive graph, Cayley graph Published: 15.10.2013; Views: 1297; Downloads: 13 Full text (0,00 KB) |