Complexity of TTP(2)

Determine the computational complexity status of the Traveling Tournament Problem with maximum trip length two, specifically whether TTP(2) belongs to the class P.

Background

The classic Traveling Tournament Problem TTP(k) seeks a minimum-distance compact double round-robin timetable in which home stands and road trips have length at most k and no game is immediately followed by its reverse fixture. The paper summarizes known complexity results: TTP(3) and TTP(k) for fixed k>3 are NP-hard, while the unconstrained version is also NP-hard. The complexity classification of the k=2 case is singled out as unresolved.

References

The complexity status of TTP(2), though, is still open.

\begin{open} Determine the computational complexity status of TTP(2), i.e., TTP(2)$\in \mathcal{P}$? \end{open}

— The Traveling Tournament Problem: An Overview  (2609.03612 - Bulck et al., 3 Sep 2026) in Section 2, subsection “Classic version of the problem”