On blockers and transversals of maximum independent sets in co-comparability graphs
BP2-STS
Published in:
- Discrete Applied Mathematics. - Elsevier BV. - 2024, vol. 356, p. 307-321
English
In this paper, we consider the following two problems: (i) Deletion Blocker(α) where we are given an undirected graph G = (V, E) and two integers k, d ≥ 1 and ask whether there exists a subset of vertices S ⊆ V with |S| ≤ k such that α(G−S) ≤ α(G)−d, that is the independence number of G decreases by at least d after having removed the vertices from S; (ii) Transversal(α) where we are given an undirected graph G = (V, E) and two integers k, d ≥ 1 and ask whether there exists a subset of vertices S ⊆ V with |S| ≤ k such that for every maximum independent set I we have |I ∩ S| ≥ d. We show that both problems are polynomial-time solvable in the class of co-comparability graphs by reducing them to the well-known Vertex Cut problem. Our results generalise a result of Chang et al. (2001) and a recent result of Hoang et al. (2023).
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Faculty
- Faculté des sciences économiques et sociales et du management
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Department
- Département d'informatique
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Language
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Classification
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Mathematics
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License
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CC BY
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Open access status
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hybrid
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Identifiers
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Persistent URL
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https://folia.unifr.ch/unifr/documents/328987
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