The purpose of this paper is to initiate study of the following problem: Let
G be a graph, and
k
1. Determine the minimum number
s of trees
T1,…,Ts,
Δ(Ti)
k,i=1,…,s, covering all vertices of
G. We conjecture: Let
G be a connected graph, and
k
2. Then the vertices of
G can be covered by
![View the MathML source View the MathML source](http://www.sciencedirect.com/cache/MiamiImageURL/B6V00-4PRHM11-6-97/0?wchp=dGLzVzz-zSkWb)
edge-disjoint trees of maximum degree
k. As a support for the conjecture we prove the statement for some values of
δ and
k.