Abstract
We consider a natural variant of the well-known Feedback Vertex Set problem, namely the problem of deleting a small subset of vertices or edges to a full binary tree. This version of the problem is motivated by real-world scenarios that are best modeled by full binary trees. We establish that both the edge and vertex deletion variants of the problem are \(\mathsf {NP}\)-hard. This stands in contrast to the fact that deleting edges to obtain a forest or a tree is equivalent to the problem of finding a minimum cost spanning tree, which can be solved in polynomial time. We also establish that both problems are \(\mathsf {FPT}\) by the standard parameter.
The authors acknowledge funding support from IIT Gandhinagar for PD and NM, and SERB (Grant No. MTR/2017/001033/MS) for NM.
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Dayal, P., Misra, N. (2019). Deleting to Structured Trees. In: Du, DZ., Duan, Z., Tian, C. (eds) Computing and Combinatorics. COCOON 2019. Lecture Notes in Computer Science(), vol 11653. Springer, Cham. https://doi.org/10.1007/978-3-030-26176-4_11
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DOI: https://doi.org/10.1007/978-3-030-26176-4_11
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