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arXiv · 1503.01098

Recognizing k-equistable graphs in FPT time

Eun Jung Kim·Martin Milanic·Oliver Schaudt
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Abstract

A graph $G = (V,E)$ is called equistable if there exist a positive integer $t$ and a weight function $w : V \to \mathbb{N}$ such that $S \subseteq V$ is a maximal stable set of $G$ if and only if $w(S) = t$. Such a function $w$ is called an equistable function of $G$. For a positive integer $k$, a graph $G = (V,E)$ is said to be $k$-equistable if it admits an equistable function which is bounded by $k$. We prove that the problem of recognizing $k$-equistable graphs is fixed parameter tractable when parameterized by $k$, affirmatively answering a question of Levit et al. In fact, the problem admits an $O(k^5)$-vertex kernel that can be computed in linear time.

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Eun Jung Kim, Martin Milanic, Oliver Schaudt. 2015-03-03. Recognizing k-equistable graphs in FPT time. https://arxiv.org/abs/1503.01098

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