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DESCRIPTION: The combinatorial properties much-loved Erdős-Rényi random gra
ph G ( n \, p )\, which has n vertices and whose edges are present indep
endently with probability p \, have been comprehensively studied in the de
cades since its introduction. In recent years\, much research has been dev
oted to the randomly perturbed graph model\, introduced in 2003 by Bohman\,
Frieze and Martin. In this talk we shall present and motivate this new mo
del of random graphs\, and then focus on the Ramsey properties of these ran
domly perturbed graphs. More precisely\, given a pair of graphs ( F \, H )
\, we ask how many random edges must be added to a dense graph G to ensur
e that any two-colouring of the edges of the perturbed graph has either a r
ed copy of F or a blue copy of G . This question was first studied in 2
006 by Krivelevich\, Sudakov and Tetali\, who answered it in the case of F
being a triangle and H being a clique. We generalise these results\, c
onsidering pairs of larger cliques\, and\, should the audience be willing (
but even otherwise)\, shall take a quick look at some of the ideas required
in our proofs. This is joint work with Andrew Treglown (Birmingham).
DTSTAMP:20181211T114600
DTSTART:20181217T141500
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9
\n 14195 Berlin \n Room 005 (Ground Floor)
SEQUENCE:0
SUMMARY:Shagnik Das (Freie Universität Berlin): Randomly perturbed Ramsey p
roblems
UID:95344199@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20181217-L-Das.html
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