Universality of random graphs and rainbow embedding

Universality of random graphs and rainbow embedding

In this paper we show how to use simple partitioning lemmas in order to embed spanning graphs in a typical member of G(n,p). Let the maximum density of a graph H be the maximum average degree of all the subgraphs of H. First, we show that for p=ω(Δ12n−1/2dlog3n), a graph G∼G(n,p) w.h.p. contains cop...

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Veröffentlicht in:Random structures & algorithms 2016-05, Vol.48 (3), p.546-564
Hauptverfasser: Ferber, Asaf, Nenadov, Rajko, Peter, Ueli
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Color
Constants
Density
embeddings
Graph theory
Graphs
Partitioning
Rainbows
random graphs
universality
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Zusammenfassung:In this paper we show how to use simple partitioning lemmas in order to embed spanning graphs in a typical member of G(n,p). Let the maximum density of a graph H be the maximum average degree of all the subgraphs of H. First, we show that for p=ω(Δ12n−1/2dlog3n), a graph G∼G(n,p) w.h.p. contains copies of all spanning graphs H with maximum degree at most Δ and maximum density at most d. For d
ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.20596