English

On some optimization problems for star-free graphs

Computational Complexity 2007-05-23 v1 Discrete Mathematics
Authors: V. G. Naidenko , Yu. L. Orlovich
View on arXiv ↗ PDF ↗

Abstract

It is shown that in star-free graphs the maximum independent set problem, the minimum dominating set problem and the minimum independent dominating set problem are approximable up to constant factor by any maximal independent set.

Keywords

graph theory graph algorithms

Cite

@article{arxiv.cs/0106048,
  title  = {On some optimization problems for star-free graphs},
  author = {V. G. Naidenko and Yu. L. Orlovich},
  journal= {arXiv preprint arXiv:cs/0106048},
  year   = {2007}
}

Comments

6 pages, in Russian

Related papers

View all related →
Data Structures and Algorithms · Computer Science
About the finding of independent vertices of a graph
Anatoly D. Plotnikov
2016-03-08
Data Structures and Algorithms · Computer Science
The Generalized Independent and Dominating Set Problems on Unit Disk Graphs
Sangram K. Jena, Ramesh K. Jallu, Gautam K. Das, Subhas C. Nandy
2020-06-30
Combinatorics · Mathematics
The minimum number of maximal independent sets in twin-free graphs
Stijn Cambie, Stephan Wagner
2024-09-17
Combinatorics · Mathematics
Maximal independent sets in graphs with given matching number
Yongtang Shi, Jianhua Tu, Ziyuan Wang
2025-06-02
Combinatorics · Mathematics
Independent domination of graphs with bounded maximum degree
Eun-Kyung Cho, Jinha Kim, Minki Kim, Sang-il Oum
2022-11-30
Combinatorics · Mathematics
The Minimum Dominating Set problem is polynomial for (claw, P8)-free graphs
Valentin Bouquet, Christophe Picouleau
2021-09-27
Combinatorics · Mathematics
Generalized domination structure in cubic graphs
Misa Nakanishi
2025-12-15
Combinatorics · Mathematics
On Minimum Dominating Sets in cubic and (claw,H)-free graphs
Valentin Bouquet, François Delbot, Christophe Picouleau, Stéphane Rovedakis
2020-02-28
Discrete Mathematics · Computer Science
Polynomial-time Algorithms for Weighted Efficient Domination Problems in AT-free Graphs and Dually Chordal Graphs
Andreas Brandstädt, Pavel Fičur, Arne Leitert, Martin Milanič
2014-11-26
Data Structures and Algorithms · Computer Science
Dominating Sets and Connected Dominating Sets in Dynamic Graphs
Niklas Hjuler, Giuseppe F. Italiano, Nikos Parotsidis, David Saulpic
2019-01-29
Distributed, Parallel, and Cluster Computing · Computer Science
A local constant factor approximation for the minimum dominating set problem on bounded genus graphs
Saeed Akhoondian Amiri, Stefan Schmid, Sebastian Siebertz
2016-02-15
Data Structures and Algorithms · Computer Science
On Relaxation of Dominant Sets
Max Koster
2024-09-27
Combinatorics · Mathematics
Complexity of Near-3-Choosability Problem
Sounaka Mishra, Rohini S, Sagar S. Sawant
2023-05-22
Data Structures and Algorithms · Computer Science
A Branch-and-Reduce Algorithm for Finding a Minimum Independent Dominating Set
Serge Gaspers, Mathieu Liedloff
2010-09-08
Discrete Mathematics · Computer Science
Distributed domination on sparse graph classes
Ozan Heydt, Simeon Kublenz, Patrice Ossona de Mendez, Sebastian Siebertz +1
2022-07-07
Combinatorics · Mathematics
Multiple vertex coverings by specified induced subgraphs
Zoltan Furedi, Dhruv Mubayi, Douglas B. West
2007-05-23
Computational Geometry · Computer Science
Approximation Algorithms for Independence and Domination on B$_1$-VPG and B$_1$-EPG Graphs
Saeed Mehrabi
2017-02-21
Data Structures and Algorithms · Computer Science
Quasi-polynomial time approximation schemes for the Maximum Weight Independent Set Problem in H-free graphs
Maria Chudnovsky, Marcin Pilipczuk, Michał Pilipczuk, Stéphan Thomassé
2023-11-15
Data Structures and Algorithms · Computer Science
On (In)approximability of MaxMin Independent Set Reconfiguration
Hung P. Hoang, Naoto Ohsaka, Rin Saito, Yuma Tamura
2026-04-30
Data Structures and Algorithms · Computer Science
Domination When the Stars Are Out
Danny Hermelin, Matthias Mnich, Erik Jan van Leeuwen, Gerhard Woeginger
2019-01-16
Distributed, Parallel, and Cluster Computing · Computer Science
Distributed Distance-$r$ Dominating Set on Sparse High-Girth Graphs
Saeed Akhoondian Amiri, Ben Wiederhake
2019-10-08
Neural and Evolutionary Computing · Computer Science
A novel evolutionary formulation of the maximum independent set problem
V. C. Barbosa, L. C. D. Campos
2007-05-23
Data Structures and Algorithms · Computer Science
Experimental Algorithm for the Maximum Independent Set Problem
Anatoly D. Plotnikov
2016-03-02
Combinatorics · Mathematics
Weighted domination models and randomized heuristics
Lukas Dijkstra, Andrei Gagarin, Vadim Zverovich
2024-01-23
Combinatorics · Mathematics
Constant-factor approximation of domination number in sparse graphs
Zdenek Dvorak
2011-10-25