Pre-assignment problem for unique minimum vertex cover on bounded clique-width graphs
Abstract
Horiyama et al. (AAAI 2024) considered the problem of generating instances with a unique minimum vertex cover under certain conditions. The Pre-assignment for Uniquification of Minimum Vertex Cover problem (shortly PAU-VC) is the problem, for given a graph $G$, to find a minimum set $S$ of vertices in $G$ such that there is a unique minimum vertex cover of $G$ containing $S$. We show that 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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.09591
- arXiv:
- arXiv:2408.09591
- Bibcode:
- 2024arXiv240809591A
- Keywords:
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- Computer Science - Data Structures and Algorithms
- E-Print:
- 19 pages, 3 figures