1. On the proper interval completion problem within some chordal subclassesFrançois Dross, Claire Hilaire, Ivo Koch, Valeria Alejandra Leoni, Nina Pardal, María Inés Lopez Pujato, Vinicius Fernandes dos Santos, 2025, original scientific article Abstract: Given a property (graph class) Π, a graph G, and an integer k, the Π-completion problem consists of deciding whether we can turn G into a graph with the property Π by adding at most k edges to G. The Π-completion problem is known to be NP-hard for general graphs when Π is the property of being a proper interval graph (PIG). In this work, we study the PIG-completion problem within different subclasses of chordal graphs. We show that the problem remains NP-complete even when restricted to split graphs. We then turn our attention to positive results and present polynomial time algorithms to solve the PIG-completion problem when the input is restricted to caterpillar and threshold graphs. We also present an efficient algorithm for the minimum co-bipartite-completion for quasi-threshold graphs, which provides a lower bound for the PIG-completion problem within this graph class.
Keywords: proper interval completion, split graph, threshold graph, quasi-threshold graph, caterpillar
Published in RUP: 06.08.2025; Views: 423; Downloads: 9
 Full text (824,75 KB)
This document has more files! More... |
2. Edge elimination and weighted graph classesJesse Beisegel, Nina Chiarelli, Ekkehard Köhler, Matjaž Krnc, Martin Milanič, Nevena Pivač, Robert Scheffler, Martin Strehler, 2020, published scientific conference contribution Keywords: edge elimination, weighted graph, split graph, threshold graph, chain graph, linear-time recognition algorithm
Published in RUP: 10.11.2020; Views: 3054; Downloads: 38
 Link to full text |
3. Linear separation of connected dominating sets in graphsNina Chiarelli, Martin Milanič, 2019, original scientific article 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, polynomial-time algorithm
Published in RUP: 04.04.2019; Views: 4811; Downloads: 167
Full text (648,51 KB) |
4. Decomposing 1-Sperner hypergraphs, with applications to graphs, Journée-séminaire de combinatoire (équipe CALIN du LIPN, Université Paris-Nord, Villetaneuse), 11. 9. 2018Martin Milanič, 2018, invited lecture at foreign university Keywords: 1-Sperner hypergraph, threshold hypergraph, decomposition, threshold graph, clique-width
Published in RUP: 30.09.2018; Views: 4652; Downloads: 26
Link to full text |
5. Decomposing 1-Sperner hypergraphs, with applications to graphs, Séminaires du Pôle 2 : Optimisation combinatoire, algorithmique", LAMSADE, Université Paris-Dauphine, 17. 9. 2018Martin Milanič, 2018, invited lecture at foreign university Keywords: 1-Sperner hypergraph, threshold hypergraph, decomposition, threshold graph, clique-width
Published in RUP: 30.09.2018; Views: 3683; Downloads: 29
Link to full text |
6. |
7. |
