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: firstname.lastname@example.org.
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
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.
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)