Max-Leaves Spanning Tree is APX-hard for Cubic Graphs
Discrete Mathematics
2009-12-02 v1 Computational Complexity
Data Structures and Algorithms
Abstract
We consider the problem of finding a spanning tree with maximum number of leaves (MaxLeaf). A 2-approximation algorithm is known for this problem, and a 3/2-approximation algorithm when restricted to graphs where every vertex has degree 3 (cubic graphs). MaxLeaf is known to be APX-hard in general, and NP-hard for cubic graphs. We show that the problem is also APX-hard for cubic graphs. The APX-hardness of the related problem Minimum Connected Dominating Set for cubic graphs follows.
Cite
@article{arxiv.0912.0226,
title = {Max-Leaves Spanning Tree is APX-hard for Cubic Graphs},
author = {Paul Bonsma},
journal= {arXiv preprint arXiv:0912.0226},
year = {2009}
}