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On the Edge-Expansion of Graphs

Published online by Cambridge University Press:  01 June 1997

NOGA ALON
NOGA ALON
Affiliation:
Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel (e-mail: noga@math.tau.ac.il)
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Abstract

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−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.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 6 , Issue 2 , June 1997 , pp. 145 - 152
Copyright
1997 Cambridge University Press

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