<F3.725e+05> J. Friedman, J. Kahn, and E. Szemer<F3.823e+05> edi,<F3.443e+05> On the second eigenvalue in random regular<F3.823e+05> graphs, in Proc. 21st Annual ACM Symposium on Theory of Computing, Seattle, WA, May 1989, pp. 587--598.  Home/Search   Document Not in Database   Summary   Related Articles

....i is a multigraph from a random configuration (when its degree sequence is given) All that remains now is to show that (15) holds with suitably high probability for M i , i # 1, conditioned on it being simple. 10.3. Eigenvalues. We will prove (15) by imitating the proof of Kahn and Szemeredi [10]. Let d = d 1 , d 2 , d n be a degree sequence with maximum # = o(n 1 2 ) and minimum # 0 such that # # # for some constant #. Strictly speaking we should be concerned with d = d 1 , d 2 , d # , but # = n o(n) whp and n is friendlier. Let M = M(F ) be the multigraph on ....

....Note that E [X # ] # (u,v)#B x u y v 2m 1 # (u,u)#B x u y u (d u 1) 2(2m 1)d u . Write S 1 and S 2 for the first and second sums in the above equation. Then S 2 # # (u,u)#B x u y u (d u 1) 2(2m 1)d u # # 1 2 4m . 31) For S 1 we follow Lemma 2. 4 in [10]. Since # u x u = # v y v = 0 we have # u,v x u y v = 0 and so # # # # # (u,v)#B x u y v # # # # = # # # # # (u,v)##B x u y v # # # # . Now # # # # # (u,v)##B x u y v # # # # # # xu yv ## 1 2 n x 2 u y 2 v x u y v # n # 1 2 # u,v x 2 u y 2 v # ....

[Article contains additional citation context not shown here]

<F3.725e+05> J. Friedman, J. Kahn, and E. Szemer<F3.823e+05> edi,<F3.443e+05> On the second eigenvalue in random regular<F3.823e+05> graphs, in Proc. 21st Annual ACM Symposium on Theory of Computing, Seattle, WA, May 1989, pp. 587--598.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC