Abstract
A graph G is called ( k, n)-pendant tree-connected, iff for any subset A of the vertex set of G with cardinality k there exist n edge-disjoint trees T 1,…, T n which contain A as set of endvertices and are vertex-disjoint with the exception of A. This is a specialization of the tree-connectivity introduced in (M. Hager, Tree-connectivity in graphs, submitted) and includes the usual vertex-connectivity for k = 2. Necessary and sufficient conditions are given for a graph to be ( k, n)-pendant tree-connected proving that κ( G)≥2 n( k + 1) implies the ( k, n)-pendant tree-connectivity and k + n + 1 is a lower bound for this implication. Then we handle the case (3,2) showing that nonplanar graphs G with κ( G)≥4, such that G-{ e} for some edge e is planar, are (3,2)-pendant tree-connected.
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