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Pre-Assignment Problem for Unique Minimum Vertex Cover on Bounded Clique-Width Graphs
- Authors
- An, Shinwoo; Chang, Yeonsu; Cho, Kyungjin; Kwon, Ojoung; Lee, Myounghwan; Oh, Eunjin; Shin, Hyeonjun
- Issue Date
- Apr-2025
- Publisher
- Association for the Advancement of Artificial Intelligence
- Citation
- Proceedings of the AAAI Conference on Artificial Intelligence, v.39, no.25, pp 26886 - 26894
- Pages
- 9
- Indexed
- SCOPUS
- Journal Title
- Proceedings of the AAAI Conference on Artificial Intelligence
- Volume
- 39
- Number
- 25
- Start Page
- 26886
- End Page
- 26894
- ISSN
- 2159-5399
2374-3468
- 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 polynomial time on split graphs and unit interval graphs.
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Related Researcher
- Kwon, O jung
- COLLEGE OF NATURAL SCIENCES (DEPARTMENT OF MATHEMATICS)