1. 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 ▫$\gamma^i < \gamma$▫. Found in: ključnih besedah Summary of found: ...\gamma(G)$▫ is known to hold for all chordal graphs and for chordless cycles of length... Keywords: Vizing's conjecture, domination number, independence-domination number, weakly chordal graph, NP-completeness, hereditary graph class, IDD-perfect graph Published: 15.10.2013; Views: 1303; Downloads: 70 Full text (0,00 KB) |
2. Nove karakterizacije v strukturni teoriji grafovTatiana Romina Hartinger, 2017, doctoral dissertation Found in: ključnih besedah Summary of found: ...graph, structural characterization of families of graphs, chordal graph, interval graph, circular arc graph, cograph,... Keywords: 1-perfectly orientable graph, structural characterization of families of graphs, chordal graph, interval graph, circular arc graph, cograph, block-cactus graph, cobipartite graph, K4-minor-free graph, outerplanar graph, graph product, Cartesian product, lexicographic product, direct product, strong product, price of connectivity, cycle transversal, path transversal Published: 09.11.2017; Views: 604; Downloads: 10 Full text (0,00 KB) |
3. Linear separation of connected dominating sets in graphsNina Chiarelli, Martin Milanič, 2019, original scientific article Found in: ključnih besedah Summary of found: ...graph, forbidden induced subgraph characterization, split graph, chordal graph, minimal cutset, minimal separator, 1-Sperner hypergraph,... Keywords: connected dominating set, connected domination, connected-domishold graph, forbidden induced subgraph characterization, split graph, chordal graph, minimal cutset, minimal separator, 1-Sperner hypergraph, threshold hypergraph, threshold Boolean function Published: 04.04.2019; Views: 336; Downloads: 99 Full text (0,00 KB) |
4. Detecting strong cliquesAdemir Hujdurović, Martin Milanič, Bernard Ries, 2019, original scientific article Found in: ključnih besedah Summary of found: ...strong clique, weakly chordal graph, line graph, cubic graph... Keywords: strong clique, weakly chordal graph, line graph, cubic graph Published: 30.06.2019; Views: 438; Downloads: 88 Full text (0,00 KB) |