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Limit theorems for monochromatic stars

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 16 Apr 2019Embargo end date: 01 Apr 2017 English Publisher:WileyJournal:Random Structures & Algorithms, volume 55, pages 831-853 (issn: 1042-9832, eissn: 1098-2418, Copyright policy )
Authors: Bhaswar B. Bhattacharya; Sumit Mukherjee;

doi: 10.1002/rsa.20856 , 10.48550/arxiv.1704.04674

arXiv: 1704.04674

Limit theorems for monochromatic stars

Abstract

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.

Related Organizations
Keywords

Combinatorial probability, Probability (math.PR), limit theorems, combinatorial probability, subgraph counts, Coloring of graphs and hypergraphs, graph coloring, FOS: Mathematics, Mathematics - Combinatorics, monochromatic subgraph, Combinatorics (math.CO), Mathematics - Probability, 05C15, 60C05, 60F05, 05D99

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
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