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3. Edge elimination schemes of weighted graph classes, Workshop on Graph Modification algorithms, experiments and new problems, 23rd - 24th January 2020, Bergen, NorwayMartin Milanič, Jesse Beisegel, Nina Chiarelli, Ekkehard Köhler, Matjaž Krnc, Nevena Pivač, Robert Scheffler, Martin Strehler, 2020, vabljeno predavanje na konferenci brez natisa Ključne besede: graph class, edge elimination scheme, sandwich monotonicity
Objavljeno v RUP: 28.05.2020; Ogledov: 1829; Prenosov: 0 |
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9. Linear separation of connected dominating sets in graphs : (extended abstract)Nina Chiarelli, Martin Milanič, 2014, objavljeni znanstveni prispevek na konferenci Ključne besede: povezana dominantna množica, hereditarni grafovski razred, dualno Spernerjev hipergraf, pragovni hipergraf, connected dominating set, hereditary graph class, dually Sperner hypergraph, treshold hypergraph
Objavljeno v RUP: 14.10.2015; Ogledov: 4121; Prenosov: 120
 Povezava na celotno besedilo |
10. A note on domination and independence-domination numbers of graphsMartin Milanič, 2013, objavljeni znanstveni prispevek na konferenci 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: 3578; Prenosov: 131
 Celotno besedilo (300,57 KB) |
