1. Graph classes closed under self-intersectionKonrad K. Dabrowski, Vadim V. Lozin, Martin Milanič, Andrea Munaro, Daniël Paulusma, Viktor Zamaraev, 2026, objavljeni znanstveni prispevek na konferenci Opis: A graph class is monotone if it is closed under taking subgraphs. A monotone class defined by finitely many obstructions has bounded treewidth if and only if one of the obstructions is a tripod, i.e. a disjoint union of subdivided claws and paths. This dichotomy also characterizes exactly those monotone graph classes for which many NP-hard graph problems admit polynomial-time algorithms. These dichotomies do not extend to the universe of all hereditary classes. This leads to the question of whether we can extend known dichotomies for monotone classes to larger families of hereditary classes. We answer this question affirmatively by considering the family of hereditary graph classes closed under self-intersection. This family is known to be located strictly between the monotone and hereditary classes. We prove a new structural characterization of graphs in self-intersection-closed classes excluding a tripod. In contrast to monotone classes excluding a tripod, these classes do not necessarily have bounded treewidth; in fact, they do not even need to be sparse. We use our characterization to give a complete dichotomy for Maximum Independent Set, and its weighted variant, on self-intersection-closed classes defined by finitely many obstructions: these problems are in P if the class excludes a tripod and NP-hard otherwise. Our dichotomy generalizes several known results on Maximum Independent Set in the literature. We also apply our characterization to obtain a dichotomy for Maximum Induced Matching on self-intersection-closed classes of bipartite graphs defined by finitely many obstructions, and for Satisfiability and Counting Satisfiability on self-intersection-closed classes of (bipartite) incidence graphs defined by finitely many obstructions. Finally, we use our characterization to obtain a dichotomy for boundedness of clique-width for self-intersection-closed classes of bipartite graphs defined by finitely many obstructions.
Ključne besede: graph classes, self-intersection closed, dichotomy, independent set, clique-width, treewidth
Objavljeno v RUP: 15.07.2026; Ogledov: 79; Prenosov: 4
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3. On the end-vertex problemJesse Beisegel, Carolin Denkert, Ekkehard Köhler, Matjaž Krnc, Nevena Pivač, Robert Scheffler, Martin Strehler, 2018, objavljeni povzetek znanstvenega prispevka na konferenci Ključne besede: graph search, maximum cardinality search, maximal neighborhood search, graph classes
Objavljeno v RUP: 28.05.2020; Ogledov: 3494; Prenosov: 113
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4. On the end-vertex problem of graph searchesJesse Beisegel, Carolin Denkert, Ekkehard Köhler, Matjaž Krnc, Nevena Pivač, Robert Scheffler, Martin Strehler, 2019, izvirni znanstveni članek Ključne besede: end-vertex, graph search, maximum cardinality search, maximal neighborhood search, graph classes
Objavljeno v RUP: 22.08.2019; Ogledov: 3548; Prenosov: 56
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5. On hereditary efficiently dominatable graphsMartin Milanič, 2011, objavljeni povzetek znanstvenega prispevka na konferenci Ključne besede: popolna koda, učinkovita dominacija, grafi z učinkovito dominantno množico, polinomski algoritmi, hereditarni grafovski razredi, perfect code, efficient domination, efficiently dominatable graphs, polynomial time algorithms, hereditary graph classes
Objavljeno v RUP: 15.10.2015; Ogledov: 6728; Prenosov: 374
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