On blockers and transversals of maximum independent sets in co-comparability graphs

Lucke, Felicia; Ries, Bernard

doi:10.1016/j.dam.2024.06.020

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Journal article

On blockers and transversals of maximum independent sets in co-comparability graphs

BP2-STS

Lucke, Felicia ORCID Université de Fribourg, Switzerland
Ries, Bernard ORCID Université de Fribourg, Switzerland

2024

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).

Faculty

Faculté des sciences économiques et sociales et du management

Department

Département d'informatique

Language