Abstract
Given a graph G = ( V , E ) with a subset S ⊆ E of edges, the edge subset feedback edge set problem is to find a smallest set F of edges such that in G ′ = ( V , E − F ) no cycle contains an edge in S. We also define a restricted version of this problem, in which no edge in S is allowed to be selected into F to form a solution. In this paper, we give a linear-time algorithm for the edge subset feedback edge set problem, and show that the restricted version is NP-hard for fixed | S | ⩾ 2 and fixed-parameter tractable with parameter being k = | F | .
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