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12. Odčitljivost digrafov in dvodelnih grafov : zaključna nalogaVladan Jovičić, 2016, undergraduate thesis Keywords: readability, overlap graph, labeling, integer linear program, distinctness, decomposition, HUB-number, two-dimensional grid graphs, toroidal grid graphs Published in RUP: 09.08.2016; Views: 2608; Downloads: 38 Link to full text This document has more files! More... |
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15. Maximum genus, connectivity, and Nebeský's theoremDan Steven Archdeacon, Michal Kotrbčík, Roman Nedela, Martin Škoviera, 2015, original scientific article Keywords: maksimalen rod, Nebeskýnov rod, Bettijevo število, povezanost, maximum genus, Nebeský theorem, Betti number, connectivity Published in RUP: 15.10.2015; Views: 2625; Downloads: 149 Link to full text |
16. A note on domination and independence-domination numbers of graphsMartin Milanič, 2013, published scientific conference contribution Abstract: 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 ▫$\gamma^i < \gamma$▫. Keywords: Vizing's conjecture, domination number, independence-domination number, weakly chordal graph, NP-completeness, hereditary graph class, IDD-perfect graph Published in RUP: 15.10.2013; Views: 3108; Downloads: 128 Full text (300,57 KB) |
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