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arXiv · 1712.08362

Connected Vertex Cover for $(sP_1+P_5)$-Free Graphs

Matthew Johnson·Giacomo Paesani·Daniel Paulusma
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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 (a graph is $H$-free if it does not contain $H$ as an induced subgraph). It is easy to see that Connected Vertex Cover is polynomial-time solvable for $P_4$-free graphs. We continue the search for tractable graph classes: we prove that it is also polynomial-time solvable for $(sP_1+P_5)$-free graphs for every integer $s\geq 0$.

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Matthew Johnson, Giacomo Paesani, Daniel Paulusma. 2017-12-22. Connected Vertex Cover for $(sP_1+P_5)$-Free Graphs. https://arxiv.org/abs/1712.08362

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