On the edge-expansion of graphs

Received It is shown that if n > n 0 (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]  N. Alon,et al.  il , , lsoperimetric Inequalities for Graphs , and Superconcentrators , 1985 .

[2]  Alexander Lubotzky,et al.  Explicit expanders and the Ramanujan conjectures , 1986, STOC '86.

[3]  Andrei Z. Broder,et al.  On the second eigenvalue of random regular graphs , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[4]  Béla Bollobás,et al.  The Isoperimetric Number of Random Regular Graphs , 1988, Eur. J. Comb..

[5]  Noga Alon,et al.  On the second eigenvalue of a graph , 1991, Discret. Math..

[6]  James B. Shearer,et al.  A Note on Bipartite Subgraphs of Triangle-Free Graphs , 1992, Random Struct. Algorithms.

[7]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.