摘要
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.
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.
