Max-Leaves Spanning Tree is APX-hard for Cubic Graphs

TL;DR

This paper proves that finding a maximum-leaves spanning tree remains APX-hard even in cubic graphs, confirming the computational difficulty of the problem in this restricted class and relating it to the hardness of the Minimum Connected Dominating Set.

Contribution

It establishes the APX-hardness of Max-Leaves Spanning Tree specifically for cubic graphs, extending the known hardness results.

Findings

Max-Leaves Spanning Tree is APX-hard for cubic graphs.

The APX-hardness of Minimum Connected Dominating Set also holds for cubic graphs.

The problem remains computationally challenging even in restricted graph classes.

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.