Improved sufficient conditions for [formula omitted]-leaf-connected graphs.

For integer k ≥ 2 , a graph G is called k -leaf-connected if | V (G) | ≥ k + 1 and given any subset S ⊆ V (G) with | S | = k , G always has a spanning tree T such that S is precisely the set of leaves of T. Thus a graph is 2-leaf-connected if and only if it is Hamilton-connected. Gurgel and Wakabayashi (1986) provided a sufficient condition based upon the size for a graph to be k -leaf-connected. In this paper, we present a new condition for k -leaf-connected graphs which improves the result of Gurgel and Wakabayashi. Meanwhile, we also extend the condition on Hamilton-connected graphs of Zhou and Wang (2017). As applications, sufficient conditions for a graph to be k -leaf-connected in terms of the (signless Laplacian) spectral radius of G or its complement are obtained. [ABSTRACT FROM AUTHOR]