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arXiv · 2408.09591

Pre-assignment problem for unique minimum vertex cover on bounded clique-width graphs

Shinwoo An·Yeonsu Chang·Kyungjin Cho·O-joung Kwon·Myounghwan Lee·Eunjin Oh·Hyeonjun Shin
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Abstract

Horiyama et al. (AAAI 2024) considered the problem of generating instances with a unique minimum vertex cover under certain conditions. The Minimum Pre-assignment for Uniquification of Minimum Vertex Cover problem (shortly Min PAU-VC) is the problem, for given a graph $G$, to find a minimum set $S$ of vertices in $G$ such that among all minimum vertex covers of $G$, exactly one contains $S$. We show that Min PAU-VC is fixed-parameter tractable parameterized by clique-width, which improves an exponential algorithm for trees given by Horiyama et al. Among natural graph classes with unbounded clique-width, we show that the problem can be solved in linear time on split graphs and unit interval graphs.

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Shinwoo An, Yeonsu Chang, Kyungjin Cho, O-joung Kwon, Myounghwan Lee, Eunjin Oh, Hyeonjun Shin. 2024-08-18. Pre-assignment problem for unique minimum vertex cover on bounded clique-width graphs. https://arxiv.org/abs/2408.09591

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