On a Spanning K-tree Containing Specified Vertices in a Graph

A k-tree is a tree with maximum degree at most k. In this paper, we give a sharp degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than t, where 1 <= t <= k. We denote by sigma(k)(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k >= 2, s >= 0 and 1 <= t <= k be integers, and suppose G is an (s + 1)-connected graph with sigma(k)(G) >= divide G divide + (k - t)s - 1. Then for any s specified vertices, G contains a spanning k-tree in which every specified vertex has degree at most t. This improves a result obtained by Matsuda and Matsumura.