A vertex labeling of a hypergraph is sum distinguishing if it uses positive integers and the sums labels taken over distinct hyperedges are distinct. Let s(H) be smallest integer N such that there sum-distinguishing H with each label at most N. The largest value all hypergraphs on n vertices m denoted s(n,m). We prove s(n,m) almost-quadratic in as long not too large. More precisely, following h...

You are handed a graph with vertices in neutral color and asked to subset of expensive paints d colors such way that only the trivial symmetry preserves classes. Your goal is minimize number needing this paint. This paper address issues surrounding your choices. A said be d-distinguishable if there exists vertex coloring so automorphism The smallest for which G called distinguishing G, denoted ...