Spanning trees with many leaves

A connected graph having large minimum vertex degree must have a spanning tree with many leaves. In particular, let l(n, k) be the maximum integer m such that every connected n-vertex graph with minimum degree at least k has a spanning tree with at least m leaves. Then l(n, 3)>= n/4 + 2, l(n, 4)>-_ (2n + 8)/5, and l(n, k) <= n 3Ln/(k + )j + 2 for all k. The lower bounds are proved by an algorithm that constructs a spanning tree with at least the desired number of leaves. Finally, l(n, k) >= (1 b In k/k)n for large k, again proved algorithmically, where b is any constant exceeding 2.5. Key words, spanning trees, vertex degrees AMS(MOS) subject classifications. 05C05, 05C35