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Chromatic number, clique subdivisions, and the conjectures of Hajós and Erdős-Fajtlowicz

✍ Scribed by Jacob Fox, Choongbum Lee, Benny Sudakov

Book ID
120912586
Publisher
Springer-Verlag
Year
2013
Tongue
English
Weight
224 KB
Volume
33
Category
Article
ISSN
0209-9683

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For any integer r \ 1, let a(r) be the largest constant a \ 0 such that if E > 0 and 0 < c < c 0 for some small c 0 =c 0 (r, E) then every graph G of sufficiently large order n and at least edges contains a copy of any (r+1)-chromatic graph H of independence number a(H) [ (a -E) log n log(1/c) .