Deleting to Structured Trees
Pratyush Dayal, Neeldhara Misra

TL;DR
This paper studies the problem of deleting vertices or edges to form a full binary tree, proving NP-hardness and fixed-parameter tractability, highlighting differences from related polynomial-time solvable problems.
Contribution
It introduces a new variant of the Feedback Vertex Set problem focused on full binary trees, establishing NP-hardness and FPT results.
Findings
Both vertex and edge deletion problems are NP-hard.
Both problems are fixed-parameter tractable (FPT).
Contrasts with polynomial-time solvability of related problems.
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 versions of the problem are NP-hard, which 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 FPT by the standard parameter.
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Optimization and Search Problems
