 
Summary: Discrete Mathematics 114 (1993) 37
NorthHolland
Bisection of trees and sequences
N. Alon, Y. Caro and I. Krasikov
School of Mathematical Sciences, Suckler Faculty of Exact Sciences, TelAaic University, Israel
Received 11 December 1988
Revised 6 May 1990
Abstract
Alon, N., Y. Caro and I. Krasikov, Bisection of trees and sequences, Discrete Mathematics 114
(1993) 337.
A graph G is called bisectable if it is an edgedisjoint union of two isomorphic subgraphs. We show
that any tree T with e edges contains a bisectable subgraph with at least e  O(e/log log e) edges. We
also show that every forest of size e, each component of which is a star, contains a bisectable
subgraph of size at least e O(log2 e).
1. Introduction
Let G be a graph with n = n(G) vertices and e = e(G) edges. The number of edges e of
G is called the size of G. G is bisectab2e if it is an edgedisjoint union of two isomorphic
subgraphs.
Let B(G) be a bisectable subgraph of maximum size of G.
The function R(G) = e(G) e(B(G)) for general graphs G has been studied by ErdBs
