A note on the minimum H-subgraph edge deletion

A. Grigoriev*, B. Marchal, N. Usotskaya

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


In this note we consider the following problem: Given a graph G and a subgraph H, what is the smallest subset E'⊆E(G) of edges in G that needs to be deleted from the graph to make it H free? Several algorithmic results are presented. First, using the general framework of Courcelle [9], we show that, for a fixed subgraph H, the problem can be solved in linear time on graphs of bounded treewidth. It is known that the constant hidden in the big-O notation of Courcelle algorithm is big which makes the approach impractical. Thus, we present two explicit linear time dynamic programming algorithms on graphs of bounded treewidth for restricted settings of the problem with reasonable constants. Third, using the linear time algorithm for graphs of bounded treewidth, we design a Baker's type polynomial time approximation scheme for the problem on planar graphs.

Original languageEnglish
Pages (from-to)399-412
JournalInternational Journal of Foundations of Computer Science
Issue number3
Publication statusPublished - 1 Jan 2015


  • Minimum edge deletion
  • H-free graph
  • bounded treewidth


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