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{{IncludeOpenProblem|Tutte's_disjoint_tree_theorem}}
In this survey we try to point out that there are still several possible directions for generalizing this these classical result.
==Capacity disjoint version==
The directed version of this conjecture is not true in general, however, it might be still interesting to find classes of graph where it holds.
A somewhat similar [[Strongly edge-disjoint arborescences|question]] is if we do not require internally node disjoint paths, but forbid only oppositely directed pairs of edges:. Note that the condition is identical to thatin Edmonds' theorem.
{{IncludeOpenProblem|Strongly edge-disjoint arborescences}}
A natural question is replacing spanning trees/arborescences by Steiner-trees/arborescences: each tree should contain a subset <math>T\subseteq V</math> of nodes, or in the directed case,
arborescence should contain directed paths from the root ''r'' to each node in a given set <math>T\subseteq V</math>.
Both in the directed and undirected cases, the question whether ''k'' disjoint Steiner-trees/arborescences exist is NP-complete already for ''k=2""''. Still, an interesting question is to find nice sufficient conditions.
Kriesell asked the following [[Kriesell's conjecture|question ]] concerning the existence of disjoint [[wikipedia:Steiner_tree|Steiner trees]]:{{IncludeOpenProblem|Disjoint Steiner-treesKriesell's conjecture}}
===Convex node sets===
