Abstract
The Connected Vertex Cover problem is to decide if a graph G has a vertex cover of size at most k that induces a connected subgraph of G. This is a well-studied problem, known to be NP-complete for restricted graph classes, and, in particular, for H-free graphs if H is not a linear forest. On the other hand, the problem is known to be polynomial-time solvable for \(sP_2\)-free graphs for any integer \(s\ge 1\). We prove that it is also polynomial-time solvable for \((sP_1+P_5)\)-free graphs for every integer \(s\ge ~0\).
This work was supported by The Leverhulme Trust (Grant RPG-2016-258).
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Johnson, M., Paesani, G., Paulusma, D. (2018). Connected Vertex Cover for \((sP_1+P_5)\)-Free Graphs. In: Brandstädt, A., Köhler, E., Meer, K. (eds) Graph-Theoretic Concepts in Computer Science. WG 2018. Lecture Notes in Computer Science(), vol 11159. Springer, Cham. https://doi.org/10.1007/978-3-030-00256-5_23
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