Summary: Discrete Mathematics 114 (1993) 3-7
Bisection of trees and sequences
N. Alon, Y. Caro and I. Krasikov
School of Mathematical Sciences, Suckler Faculty of Exact Sciences, Tel-Aaic University, Israel
Received 11 December 1988
Revised 6 May 1990
Alon, N., Y. Caro and I. Krasikov, Bisection of trees and sequences, Discrete Mathematics 114
A graph G is called bisectable if it is an edge-disjoint 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).
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 edge-disjoint union of two isomorphic
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