Independent Feedback Vertex Sets for Graphs of Bounded Diameter
Data Structures and Algorithms
2017-08-01 v1 Discrete Mathematics
Combinatorics
Abstract
The Near-Bipartiteness problem is that of deciding whether or not the vertices of a graph can be partitioned into sets and , where is an independent set and induces a forest. The set in such a partition is said to be an independent feedback vertex set. Yang and Yuan proved that Near-Bipartiteness is polynomial-time solvable for graphs of diameter 2 and NP-complete for graphs of diameter 4. We show that Near-Bipartiteness is NP-complete for graphs of diameter 3, resolving their open problem. We also generalise their result for diameter 2 by proving that even the problem of computing a minimum independent feedback vertex is polynomial-time solvable for graphs of diameter 2.
Keywords
Cite
@article{arxiv.1707.09383,
title = {Independent Feedback Vertex Sets for Graphs of Bounded Diameter},
author = {Marthe Bonamy and Konrad K. Dabrowski and Carl Feghali and Matthew Johnson and Daniel Paulusma},
journal= {arXiv preprint arXiv:1707.09383},
year = {2017}
}