1. On {k}-Roman graphsKenny Bešter Štorgel, Nina Chiarelli, Lara Fernández, J. Pascal Gollin, Claire Hilaire, Valeria Alejandra Leoni, Martin Milanič, 2025, objavljeni znanstveni prispevek na konferenci Opis: For a positive integer k, a {k}-Roman dominating function of a graph G = (V, E) is a function f : V → {0, 1, . . . , k} satisfying f (N(v)) ≥ k for each vertex v ∈ V with f (v) = 0. Every graph G satisfies γ{Rk}(G) ≤ kγ(G), where γ{Rk}(G) denotes the minimum weight of a {k}-Roman dominating function of G and γ(G) is the domination number of G. In this work we study graphs for which the equality is reached, called {k}-Roman graphs. This extends the concept of {k}-Roman trees studied by Wang et al. in 2021 to gen- eral graphs. We prove that for every k ≥ 3, the problem of recognizing {k}-Roman graphs is NP-hard, even when restricted to split graphs. We provide partial answers to the question of which split graphs are {2}-Roman: we characterize {2}-Roman split graphs that can be decomposed with respect to the split join operation into two smaller split graphs and classify the {k}-Roman property within two specific families of split graphs that are prime with respect to the split join operation: suns and their complements.
Ključne besede: graph domination, {k}-Roman domination, {k}-Roman graph, split graph, split join, NP-completeness
Objavljeno v RUP: 16.12.2025; Ogledov: 204; Prenosov: 2
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3. Allocating indivisible items with minimum dissatisfaction on preference graphsNina Chiarelli, Clément Jean Dallard, Andreas Darmann, Stefan Lendl, Martin Milanič, Peter Muršič, Nevena Pivač, Ulrich Pferschy, 2021, objavljeni znanstveni prispevek na konferenci Ključne besede: fair division, partial order, preference graph
Objavljeno v RUP: 29.10.2021; Ogledov: 3921; Prenosov: 24
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4. Strong cliques in diamond-free graphsNina Chiarelli, Berenice Martínez-Barona, Martin Milanič, Jérôme Monnot, Peter Muršič, 2020, izvirni znanstveni članek Ključne besede: maximal clique, maximal stable set, diamond-free graph, strong clique, simplicial clique, strongly perfect graph, CIS graph, NP-hard problem, polynomial-time algorithm, Erdős-Hajnal property
Objavljeno v RUP: 17.12.2020; Ogledov: 3775; Prenosov: 162
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5. Strong cliques in diamond-free graphsNina Chiarelli, Berenice Martínez-Barona, Martin Milanič, Jérôme Monnot, Peter Muršič, 2020, objavljeni znanstveni prispevek na konferenci Ključne besede: maximal clique, maximal stable set, diamond-free graph, strong clique, simplicial clique, CIS graph, NP-hard problem, linear-time algorithm, Erdős-Hajnal property
Objavljeno v RUP: 10.11.2020; Ogledov: 3224; Prenosov: 60
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6. Edge elimination and weighted graph classesJesse Beisegel, Nina Chiarelli, Ekkehard Köhler, Matjaž Krnc, Martin Milanič, Nevena Pivač, Robert Scheffler, Martin Strehler, 2020, objavljeni znanstveni prispevek na konferenci Ključne besede: edge elimination, weighted graph, split graph, threshold graph, chain graph, linear-time recognition algorithm
Objavljeno v RUP: 10.11.2020; Ogledov: 3048; Prenosov: 38
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9. 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: 3054; Prenosov: 0 |
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