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On the Edge-Expansion of Graphs

Published online by Cambridge University Press:  01 June 1997

Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel (e-mail:


It is shown that if n>n0(d) then any d-regular graph G=(V, E) on n vertices contains a set of u=[lfloor ]n/2[rfloor ] vertices which is joined by at most (d/2−cd)u edges to the rest of the graph, where c>0 is some absolute constant. This is tight, up to the value of c.

Research Article
1997 Cambridge University Press

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