Optimal constant in Steiner forest packing

Determine the optimal constant in the Steiner forest packing guarantee that follows from pairwise connectivity, improving the currently known bound of approximately f/16 disjoint forests toward the required f+1 forests, and determine the corresponding bound for Steiner trees.

Background

The paper’s construction relies on packing Steiner forests in a fault-tolerant connectivity preserver. Existing results provide only a constant-factor fraction of the desired number of forests in the general setting, while the exact packing threshold is unknown even for Steiner trees. The authors avoid this unresolved issue through an edge-doubling and Eulerian-graph argument, but identify the packing constant as an independent open problem.

References

improving the constant in Steiner forest packing is a fascinating open problem, and the correct bound is not even known for Steiner trees.

— Light Edge Fault Tolerant Graph Spanners  (2502.10890 - Bodwin et al., 15 Feb 2025) in Section 2, subsection “Steiner Forest Packing”

Whether a removal lemma in the style of Theorem~\ref{thm:devosetal} can be obtained for ADSTP is a long-standing open problem Problem~5.5.

— Property Testing for Recursive Query Languages  (2609.03908 - Adler et al., 3 Sep 2026) in Section 5, paragraph beginning “Arc-Disjoint Directed Steiner tree packing”

In, Kriesell conjectured that a stronger result holds for any $2k$-edge-connected vertex set, together with the corresponding generalization of spanning trees, namely, Steiner trees.

— Kriesell's conjecture for infinite graphs  (2609.11534 - Aurichi et al., 10 Sep 2026) in Section 1, Introduction; Conjecture 1 (labelled \ref{kriesell})