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Title I discussed these ki A rolling stone is w
Date 2014-02-18 14:43:46 2014-02-18 15:00:49
Editor Anonymous Anonymous
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2014-02-18 14:43:46 by Anonymous / Edit this version
2014-02-18 15:00:49 by Anonymous / Edit this version
t1I discussed these kinds of Achlioptas pocress varit1A rolling stone is worth two in the bush, thanks t
>ations with Po-Shen Loh back in 2008.  According t>o this <a href="http://iinjtw.com">arielct.</a>
>o my notes, the most natural variation is to pick  
>a k-star u.a.r. and get to keep an edge.  (I wrote 
>, "The advantage of this model is that it is 'clea 
>r' what the optimal strategy for avoiding the grow 
>th of a giant component ... should be: add the edg 
>e that connects to the smallest component.")  The  
>next variation is to pick a random triangle, and g 
>et to keep two of the three edges.  The third vari 
>ant in my notes, which seems to specialize the fir 
>st, is to pick choose one of two edges that share  
>one vertex, i.e., a uniformly random path P_2.  Th 
>is seems to be what you consider.  Finally, a last 
> variation is to pick some subset of the edges of  
>a random graph H.  (And there is some sort of quan 
>tum version, too.)  As far as I could tell, the ar 
>guments didn't look sufficiently different from [K 
>rivelevich, Loh, Sudakov 07] for any of these alte 
>rnatives to be compelling, but I just thought I wo 
>uld mention them. 


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