Irena Hrastnik Ladinek (Author), Janez Žerovnik (Author)

Abstract

Cyclic bundle Hamiltonicity ▫$cbH(G)$▫ of a graph ▫$G$▫ is the minimal ▫$n$▫ for which there is an automorphism ▫$\alpha$▫ of ▫$G$▫ such that the graph bundle ▫$C_n\Box^{\alpha} G$▫ is Hamiltonian. We define ▫$\nabla (\tilde{G}_{\alpha})_{\min}$▫, an invariant that is related to the maximal vertex degree of spanning trees suitably involving the symmetries of ▫$G$▫ and prove ▫$cbH(G) \leq \nabla(\tilde{G}_{\alpha})_{min} \leq cbH(G)+1$▫ for any non-trivial connected graph ▫$G$▫.

Keywords

kartezični produkt;kartezični grafovski sveženj;hamiltonski graf;Cartesian product;Cartesian graph bundle;Hamiltonian graph;

Data

Language: English
Year of publishing:
Typology: 0 - Not set
Organization: UL FS - Faculty of Mechanical Engineering
UDC: 519.17
COBISS: 15837017 Link will open in a new window
ISSN: 2232-2094
Parent publication: Preprint series
Views: 49
Downloads: 6
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Other data

Secondary language: English
Secondary keywords: kartezični produkt;kartezični grafovski sveženj;hamiltonski graf;
URN: URN:SI:UM:
Type (COBISS): Not categorized
Pages: str. 1-9
Volume: Vol. 49
Issue: št. 1139
Chronology: 2011
ID: 1475340