Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=50292#.VDSRfVfHRK0 Author(s) Azer Akhmedov , Warren Shreve Affiliation(s) Department of Mathematics, North Dakota State University, Fargo, ND, USA . ABSTRACT We prove that a random labeled (unlabeled) tree is balanced. We also prove that random labeled and unlabeled trees are strongly k -balanced for any k ≥ 3. Definition : Color the vertices of graph G with two colors. Color an edge with the color of its endpoints if they are colored with the same color. Edges with different colored endpoints are left uncolored. G is said to be balanced if neither the number of vertices nor and the number of edges of the two different colors differs by more than one. ...
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