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41 papers · 1 filter
Deterministic approximate counting of colorings with fewer than colors via absence of zeros
Ferenc Bencs, Khallil Berrekkal, Guus Regts
Let be integers. We prove that there exists such that if , then there exists an open set that contains the i…
On the threshold for Szemerédi's theorem with random differences
Jop Briët, Davi Castro-Silva
Using recent developments on the theory of locally decodable codes, we prove that the critical size for Szemerédi's theorem with random differences is bounded from above by $N^{1-\…
Semidefinite approximations for bicliques and biindependent pairs
Monique Laurent, Sven Polak, Luis Felipe Vargas
We investigate some graph parameters dealing with biindependent pairs in a bipartite graph , i.e., pairs where , …
A recursive theta body for hypergraphs
Davi Castro-Silva, Fernando Mário de Oliveira Filho, Lucas Slot +1
The theta body of a graph, introduced by Grötschel, Lovász, and Schrijver in 1986, is a tractable relaxation of the independent-set polytope derived from the Lovász theta number. I…
The maximum cardinality of trifferent codes with lengths 5 and 6
Stefano Della Fiore, Alessandro Gnutti, Sven Polak
A code is said to be trifferent with length when for any three distinct elements of there exists a coordinate in which they…
A recursive Lovász theta number for simplex-avoiding sets
Davi Castro-Silva, Fernando Mário de Oliveira Filho, Lucas Slot +1
We recursively extend the Lovász theta number to geometric hypergraphs on the unit sphere and on Euclidean space, obtaining an upper bound for the independence ratio of these hyper…