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1.
On domination numbers of graph bundles
Blaž Zmazek, Janez Žerovnik, 2005

Opis: Let ▫$gamma(G)$▫ be the domination number of a graph ▫$G$▫. It is shown that for any ▫$k ge 0$▫ there exists a Cartesian graph bundle ▫$B Box_varphi F$▫ such that ▫$gamma(B Box_varphi F) = gamma(B)gamma(F) - 2k$▫. The domination numbers of Cartesian bundles of two cycles are determined exactly when the fibre graph is a triangle or a square. A statement similar to Vizing's conjecture on strong graph bundles is shown not to be true by proving the inequality ▫$gamma(B boxtimes_varphi F) le gamma(B)gamma(F)$▫ for strong graph bundles. Examples of graphs ▫$B$▫ and ▫$F$▫ with ▫$gamma(B boxtimes_varphi F) < gamma(B)gamma(F)$▫ are given.
Ključne besede: matematika, teorija grafov, kartezični produkt grafov, dominantno število, dominantna množica, grafovski sveženj, mathematics, graph theory, graph bundle, dominating set, domination number, Cartesian product
Objavljeno: 10.07.2015; Ogledov: 531; Prenosov: 58
URL Povezava na celotno besedilo

2.
On connectedness and hamiltonicity of direct graph bundles
Irena Hrastnik Ladinek, Janez Žerovnik, 2012, izvirni znanstveni članek

Opis: A necessary and sufficient condition for connectedness of direct graph bundles where the fibers are cycles is given. It is also proved that all connected direct graph bundles ▫$X=C_stimes^{alpha}C_t$▫ are Hamiltonian.
Ključne besede: direktni produkt grafov, direktni grafovski sveženj, hamiltonski graf, povezan graf, direct graph product, direct graph bundle, Hamiltonian graph, connected graph, reflection, cyclic ▫$ell$▫-shift
Objavljeno: 10.07.2015; Ogledov: 337; Prenosov: 20
URL Povezava na celotno besedilo

3.
Cyclic bundle Hamiltonicity
Irena Hrastnik Ladinek, Janez Žerovnik, 2011

Opis: 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 ▫$C_nBox^{alpha} G$▫ 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 ▫$G$▫.
Ključne besede: kartezični produkt, kartezični grafovski sveženj, hamiltonski graf, Cartesian product, Cartesian graph bundle, Hamiltonian graph
Objavljeno: 10.07.2015; Ogledov: 463; Prenosov: 58
URL Povezava na celotno besedilo

4.
On connectivity and hamiltonicity of direct graph bundles
Irena Hrastnik Ladinek, Janez Žerovnik, 2011

Opis: A necessary and sufficient condition for connectedness of direct graph bundles where the fibers are cycles is given. It is also proved that all connected direct graph bundles ▫$X=C_stimes^{alpha}C_t$▫ are Hamiltonian.
Ključne besede: direktni produkt grafov, direktni grafovski sveženj, hamiltonski graf, povezan graf, direct graph product, Cartesian graph bundle, Hamiltonian graph, connected graph, reflection, cyclic ▫$ell$▫-shift
Objavljeno: 10.07.2015; Ogledov: 278; Prenosov: 11
URL Povezava na celotno besedilo

5.
Efficacy of a bundle approach in preventing the incidence of ventilator associated pneumonia (VAP)
Sandra Burja, Tina Belec, Nika Bizjak, Jernej Mori, Andrej Markota, Andreja Sinkovič, 2017, izvirni znanstveni članek

Opis: Ventilator-associated pneumonia (VAP) is a potentially preventable iatrogenic illness that may develop following mechanical ventilation. A bundle for the prevention of VAP consists of different measures which may vary between institutions, and may include: elevation of the head of the bed, oral care with chlorhexidine, subglottic suctioning, daily assessment for extubation and the need for proton-pump inhibitors, use of closed suction systems, and maintaining endotracheal cuff pressure at 25 cmH2O. Our aim was to determine the efficacy of a VAP prevention bundle, consisting of the above-mentioned measures, by evaluating the incidence of VAP before (no-VAP-B group) and after (VAP-B group) the introduction of the bundle. We retrospectively evaluated the data for patients who were mechanically ventilated with an endotracheal tube, in the period between 1 September and 31 December 2014 (no-VAP-B group, n = 55, 54.5% males, mean age 67.8 ± 14.5 years) and between 1 January to 30 April 2015 (VAP-B group, n = 74, 62.1% males, mean age 64.8 ± 13.7 years). There were no statistically significant differences between no-VAP-B and VAP-B groups in demographic data, intensive care unit (ICU) mortality, hospital mortality, duration of ICU treatment, and duration of mechanical ventilation. No significant differences in the rates of VAP and early VAP (onset ≤7 days after intubation) were found between no-VAP-B and VAP-B groups (41.8% versus 25.7%, p = 0.06 and 10.9% versus 12.2%, p > 0.99, respectively). However, a significant decrease in the late VAP (onset >8 days after intubation) was found in VAP-B group compared to no-VAP-B group (13.5% versus 30.9%, p = 0.027). Overall, our results support the use of VAP prevention bundle in clinical practice.
Ključne besede: ventilator-associated pneumonia, VAP, primary prevention, epidemiology, medical devices, intratracheal intubation, bundle
Objavljeno: 13.11.2017; Ogledov: 441; Prenosov: 160
.pdf Celotno besedilo (96,15 KB)
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