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DESCRIPTION: In a two-colouring of the edges of the complete graph on the n
atural numbers\, what is the densest monochromatic infinite path that we ca
n always find? We measure the density of a path by the upper asymptotic den
sity of its vertex set. This question was first studied by Erdös and Galvin
\, who proved that the best density is between 2/3 and 8/9. In this talk we
settle this question by proving that we can always find a monochromatic pa
th of upper density at least (12+sqrt(8))/17=0.87226…\, and constructing a
two-colouring in which no denser path exists. This represents joint work wi
th Jan Corsten\, Louis DeBiasio and Richard Lang.
DTSTAMP:20181204T195500
DTSTART:20181210T160000
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9
\n 14195 Berlin \n Room 005 (Ground Floor)
SEQUENCE:0
SUMMARY:Ander Lamaison (Freie Universität Berlin): Ramsey density of infini
te paths
UID:94647887@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20181210-C-Lamaison.html
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