1. Avoidable vertices and edges in graphsJesse Beisegel, Maria Chudnovsky, Vladimir Gurvich, Martin Milanič, Mary Agnes Milanič, 2019, published scientific conference contribution Keywords: simplicial vertex, avoidable vertex, avoidable edge, avoidable path, maximum weight clique problem, polynomial-time algorithm, hole-cyclically orientable graph Published in RUP: 20.08.2019; Views: 2273; Downloads: 158 Link to full text |
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3. Nove karakterizacije v strukturni teoriji grafov : 1-popolno usmerljivi grafi, produktni grafi in cena povezanostiTatiana Romina Hartinger, 2017, doctoral dissertation Keywords: 1-perfectly orientable graph, structural characterization of families of graphs, chordal graph, interval graph, circular arc graph, cograph, block-cactus graph, cobipartite graph, K4-minor-free graph, outerplanar graph, graph product, Cartesian product, lexicographic product, direct product, strong product, price of connectivity, cycle transversal, path transversal Published in RUP: 09.11.2017; Views: 2998; Downloads: 41 Link to full text |
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8. 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. Keywords: graph theory, Hamilton cycle, Hamilton path, n-HC-extendable, strongly n-HP-extendable, weakly n-HP-extendable, Cayley graph, abelian group Published in RUP: 15.10.2013; Views: 3058; Downloads: 145 Link to full text |
9. 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. Keywords: graph theory, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group Published in RUP: 15.10.2013; Views: 3671; Downloads: 41 Link to full text |
10. Recent trends and future directions in vertex-transitive graphsKlavdija Kutnar, Dragan Marušič, 2008, original scientific article Abstract: 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. Keywords: vertex-transitive graph, arc-transitive graph, half-arc-transitive graph, Hamilton cycle, Hamilton path, semiregular group, (im)primitive group Published in RUP: 15.10.2013; Views: 3510; Downloads: 136 Full text (183,49 KB) |