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Treewidth versus clique number in graph classes with a forbidden structure
Clément Jean Dallard, Martin Milanič, Kenny Štorgel, 2020, objavljeni znanstveni prispevek na konferenci

Ključne besede: graph class, treewidth, clique number
Objavljeno v RUP: 10.11.2020; Ogledov: 1189; Prenosov: 34
URL Povezava na celotno besedilo

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Minimal separators in graph classes defined by small forbidden induced subgraphs
Martin Milanič, Nevena Pivač, 2019, objavljeni znanstveni prispevek na konferenci

Ključne besede: minimal separator, hereditary graph class, forbidden induced subgraph
Objavljeno v RUP: 16.10.2019; Ogledov: 1475; Prenosov: 104
URL Povezava na celotno besedilo

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The price of connectivity for cycle transversals
Tatiana Romina Hartinger, Matthew Johnson, Martin Milanič, Daniël Paulusma, 2015, objavljeni znanstveni prispevek na konferenci

Ključne besede: price of connectivity, hereditary graph class, path, cycle, transversal
Objavljeno v RUP: 08.08.2016; Ogledov: 2745; Prenosov: 120
URL Povezava na celotno besedilo

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Graph classes : from practice to theory
Martin Milanič, 2015, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Ključne besede: uporaba teorije grafov, razred grafov, pragoven graf, problem nahrbtnika, application of graph theory, graph class, threshold graph, knapsack problem
Objavljeno v RUP: 08.08.2016; Ogledov: 2269; Prenosov: 15
URL Povezava na celotno besedilo

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A note on domination and independence-domination numbers of graphs
Martin 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: 2916; Prenosov: 128
.pdf Celotno besedilo (300,57 KB)

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