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

  • Matthew Johnson
  • Giacomo PaesaniEmail author
  • Daniël Paulusma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11159)


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 \(s\ge ~0\).


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Matthew Johnson
    • 1
  • Giacomo Paesani
    • 1
    Email author
  • Daniël Paulusma
    • 1
  1. 1.Department of Computer ScienceDurham UniversityDurhamUK

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