A connected graph having large minimum v ertex degree must ha ve a spanning tree with man y leaves. Inparticular, let l(n, k) be the maximum inte ger m such that e very connectedn-vertex graph with minimum degree at least k has a spanning tree with at leastm leaves. Thenl(n, 3) ≥ n/4 + 2, l(n, 4) ≥ (2n + 8) /5, andl(n, k) ≤ n − 3n/(k +1) + 2 for all k. The lower bounds are proved by an algorithm that constructs a spanning tree with at least the desired number of lea ves. Finally, l(n, k) ≥ (1… CONTINUE READING