On some optimization problems for star-free graphs
V.G. Naidenko, Yu.L. Orlovich
TL;DR
This paper demonstrates that for star-free graphs, key optimization problems like maximum independent set, minimum dominating set, and minimum independent dominating set can be approximated within a constant factor using any maximal independent set.
Contribution
It establishes approximation bounds for several fundamental problems in star-free graphs, linking maximal independent sets to near-optimal solutions.
Findings
Approximation of maximum independent set within a constant factor.
Approximation of minimum dominating set within a constant factor.
Approximation of minimum independent dominating set within a constant factor.
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.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Complexity and Algorithms in Graphs