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Combinatorics, Probability and Computing (1993) 11, 110 Copyright c 1993 Cambridge University Press
 

Summary: Combinatorics, Probability and Computing (1993) 11, 110
Copyright c 1993 Cambridge University Press
On the edge-expansion of graphs
N OGA A L ON
Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences,
Tel Aviv University, Tel Aviv, Israel. Email: noga@math.tau.ac.il.
Received
It is shown that if n > n0(d) then any d-regular graph G = (V, E) on n vertices contains a set of u = n/2
vertices which is joined by at most ( d
2
- c

d)u edges to the rest of the graph, where c > 0 is some absolute
constant. This is tight, up to the value of c.
1. Introduction
For a graph G = (V, E) and for two disjoint subsets U, W of V , let e(U, W) denote the number of edges
between U and W. The edge expansion coefficient i(G) of G is defined by
i(G) = Min
e(U, V - U)
|U|

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics