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Ključne besede: readability, overlap graph, labeling, integer linear program, distinctness, decomposition, HUB-number, two-dimensional grid graphs, toroidal grid graphs
Objavljeno v RUP: 09.08.2016; Ogledov: 2628; Prenosov: 38
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Ključne besede: mathematical model, SIR model, epidemic, influenza, basic reproduction number
Objavljeno v RUP: 15.10.2015; Ogledov: 3273; Prenosov: 20
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Opis: Vizing's conjecture is true for graphs ▫$G$▫ satisfying ▫$\gamma^i(G) = \gamma(G)$▫, where ▫$\gamma(G)$▫ is the domination number of a graph ▫$G$▫ and ▫$\gamma^i(G)$▫ is the independence-domination number of ▫$G$▫, that is, the maximum, over all independent sets ▫$I$▫ in ▫$G$▫, of the minimum number of vertices needed to dominate ▫$I$▫. The equality ▫$\gamma^i(G) = \gamma(G)$▫ is known to hold for all chordal graphs and for chordless cycles of length ▫$0 \pmod{3}$▫. We prove some results related to graphs for which the above equality holds. More specifically, we show that the problems of determining whether ▫$\gamma^i(G) = \gamma(G) = 2$▫ and of verifying whether ▫$\gamma^i(G) \ge 2$▫ are NP-complete, even if ▫$G$▫ is weakly chordal. We also initiate the study of the equality ▫$\gamma^i = \gamma$▫ in the context of hereditary graph classes and exhibit two infinite families of graphs for which ▫$\gamma^i < \gamma$▫.
Ključne besede: Vizing's conjecture, domination number, independence-domination number, weakly chordal graph, NP-completeness, hereditary graph class, IDD-perfect graph
Objavljeno v RUP: 15.10.2013; Ogledov: 3119; Prenosov: 128
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Ključne besede: number of firms, ownership, inactive firms, firm size, manufacturing, Slovenia
Objavljeno v RUP: 15.10.2013; Ogledov: 2554; Prenosov: 64
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