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...
AbstractThe Erds-Ginzburg-Ziv Problem is a classical extremal problem in discrete geometry. Givenpositive integers m and n, the problem asks about the smallest number s such that among any spoints in the integer lattice Z" one can find m points whose centroid is again a lattice point. Despiteof a lot of attention over the last 50 years, this problem is stil wide open. For fixed dimension nAlon ...