Hypergraph Turan problem
March 21 to March 25, 2011
American Institute of Mathematics,
San Jose, California
and Benny Sudakov
This workshop will be devoted to the study of the
hypergraph Turan function ex(n,F), the maximum size of an F-free
k-hypergraph on n vertices. Although this fundamental problem of
extremal combinatorics was introduced by Paul Turan in 1941, it is
still wide open in general. A number of powerful methods and
techniques were developed or sharpened in recent years in order to
attack various combinatorial problems (such as hypergraph regularity,
flag algebras, or hypergraph stability). The purpose of the workshop
is to focus this machinery on solving some imporant Turan-type
questions for hypergraphs.
Two notable old problems that may be approachable by modern
methods include the Tetrahedron Conjecture of Turan from 1941 and
the (6,3)-problem of Ruzsa and Szemeredi from 1978.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
Papers arising from the workshop:
Linear trees in uniform hypergraphs
by Zoltan Furedi, European J. Combin. 35 (2014), 264-272 MR3090501
Choosability with separation of complete multipartite graphs and hypergraphs
by Zoltan Feredi, Alexandr Kostochka, and Mohit Kumbhat, J. Graph Theory 76 (2014), no. 2, 129-137 MR3190269
Asymptotic improvements to the lower bound of certian bipartite Turán numbers
by Simeon Ball and Valentina Pepe, Combin. Probab. Comput. 21 (2012), no. 3, 323-329 MR2912785
On possible Turán densities
by Oleg Pikhurko, Israel J. Math. 201 (2014), no. 1, 415-454 MR3265290
A problem of Erdős on the minimum number of $k$-cliques
by Shagnik Das, Hao Huang, Jie Ma, Humberto Naves, and Benny Sudakov , Duke Math. J. 162 (2013), no. 15, 2903-2927 MR3161307
Two extensions of Ramsey's theorem
by David Conlon, Jacob Fox, and Benny Sudakov
On independent sets in hypergraphs
by Alexander Kostochka, Dhruv Mubayi, and Jacques Versatraete, Random Structures Algorithms 44 (2014), no. 2, 224-239 MR3158630
Upper bounds on the size of 4- and 6-cycle-free subgraphs of the hypercube
by József Balogh, Ping Hu, Bernard Lidický, and Hong Liu, European J. Combin. 35 (2014), 75-85 MR3090487