
extremal combinatorics
Sidorenko's Conjecture ★★★
Author(s): Sidorenko
Conjecture For any bipartite graph
and graph
, the number of homomorphisms from
to
is at least
.





Keywords: density problems; extremal combinatorics; homomorphism
Turán Problem for $10$-Cycles in the Hypercube ★★
Author(s): Erdos
Problem Bound the extremal number of
in the hypercube.

Keywords: cycles; extremal combinatorics; hypercube
Extremal $4$-Neighbour Bootstrap Percolation in the Hypercube ★★
Problem Determine the smallest percolating set for the
-neighbour bootstrap process in the hypercube.

Keywords: bootstrap percolation; extremal combinatorics; hypercube; percolation
Saturated $k$-Sperner Systems of Minimum Size ★★
Author(s): Morrison; Noel; Scott
Question Does there exist a constant
and a function
such that if
, then every saturated
-Sperner system
has cardinality at least
?






Keywords: antichain; extremal combinatorics; minimum saturation; saturation; Sperner system
