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Title: Limit theorems for monochromatic stars

LetT(K1,r,Gn) be the number of monochromatic copies of ther‐starK1,rin a uniformly random coloring of the vertices of the graphGn. In this paper we provide a complete characterization of the limiting distribution ofT(K1,r,Gn), in the regime whereis bounded, for any growing sequence of graphsGn. The asymptotic distribution is a sum of mutually independent components, each term of which is a polynomial of a single Poisson random variable of degree at mostr. Conversely, any limiting distribution ofT(K1,r,Gn) has a representation of this form. Examples and connections to the birthday problem are discussed.

 
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NSF-PAR ID:
10091523
Author(s) / Creator(s):
 ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Random Structures & Algorithms
Volume:
55
Issue:
4
ISSN:
1042-9832
Page Range / eLocation ID:
p. 831-853
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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