On covering vertices of a graph by trees Original Research Article

The purpose of this paper is to initiate study of the following problem: Let G be a graph, and image. Determine the minimum number s of trees image, image, covering all vertices of image. We conjecture: Let G be a connected graph, and image. Then the vertices of G can be covered by image edge-disjoint trees of maximum degree image. As a support for the conjecture we prove the statement for some values of image and image.