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Title: Disproof of a packing conjecture of Alon and Spencer

A 1992 conjecture of Alon and Spencer says, roughly, that the ordinary random graphGn,1/2typically admits a covering of a constant fraction of its edges by edge‐disjoint, nearly maximum cliques. We show that this is not the case. The disproof is based on some (partial) understanding of a more basic question: forandA1,…,Atchosen uniformly and independently from thek‐subsets of {1,…,n}, what can one say aboutOur main concern is trying to understand how closely the answers to this and a related question about matchings follow heuristics gotten by pretending that certain (dependent) choices are made independently.

 
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Award ID(s):
1502650
NSF-PAR ID:
10114264
Author(s) / Creator(s):
 ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Random Structures & Algorithms
Volume:
55
Issue:
3
ISSN:
1042-9832
Page Range / eLocation ID:
p. 531-544
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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