AbstractIn the early 1980s, Erdos and Ss, initiated the study of the classical Turn problem with auniformity condition: the uniform Turn density of a hypergraph H is the infimum over all d for whichany sufficiently large hypergraph with the property that all its linear-size subhypergraphs havedensity at least d contains H. In particular, they raised the questions of determining the uniformTurn ...
AbstractIn discrepancy theory, the basic question is whether a structure can be partitioned in a balancedway, or if there is always some discrepancy no matter how the partition is made.in the context ofgraph theory, a well-studied question is whether for a given host graph, any 2-colouring of its edgesmust contain a specified subgraph "with high discrepancy", meaning that within this subgraph o...