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Kong, M.C., Lee, S.-M., Seah, E. and Tang, A. (2008) A Complete Characterization of Balanced Graphs (English Summary). Journal of Combinatorial Mathematics and Combinatorial Computing, 66, 225-236.

has been cited by the following article:

• TITLE: Balance in Random Trees

  AUTHORS: Azer Akhmedov, Warren Shreve

  KEYWORDS: Random Trees, Balance, Equicolorable Graphs

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.4 No.4, October 6, 2014

  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.