Article Dans Une Revue Discrete Applied Mathematics Année : 2025

On the hardness of problems around s-clubs on split graphs

Résumé

We investigate the complexity of problems related to s-clubs. Given a graph, an s-club is a subset of vertices such that the subgraph induced by it has diameter at most s. We show that partitioning a split graph into two 2-clubs is NP-hard. Moreover, we prove that finding the minimum number of edges to add to a split graph in order to obtain a diameter of at most 2 is W[2]-hard with respect to the number of edges to add. Finally we show that finding the minimum number of edges to keep within a split graph of diameter 2 or 3 in order to maintain its diameter is NP-complete.

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hal-04941471 , version 1 (11-02-2025)

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Cristina Bazgan, Pinar Heggernes, André Nichterlein, Thomas Pontoizeau. On the hardness of problems around s-clubs on split graphs. Discrete Applied Mathematics, 2025, 364, pp.247-254. ⟨10.1016/j.dam.2025.01.023⟩. ⟨hal-04941471⟩
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