Decomposition into two trees with orientation constraints

TL;DR

This paper proves that partitioning a graph's edges into two oriented spanning trees under certain constraints is NP-complete, disproving a previous conjecture and highlighting computational complexity in graph theory.

Contribution

It establishes the NP-completeness of a specific graph decomposition problem with orientation constraints, challenging prior conjectures.

Findings

Partitioning into two oriented spanning trees is NP-complete.

Disproves Recski's conjecture on this problem.

Highlights computational difficulty in graph decompositions.

Abstract

We prove that deciding whether the edge set of a graph can be partitionned into two spanning trees with orientation constraints is NP-complete. If P $\neq$ NP then this disproves a conjecture of Recski.