2015/03/21 by Dudek, Andrzej, La Fleur, Steven, Mubayi, Dhruv +1 · 1 citation
#05C55 #05D10 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1503.06304
The size-Ramsey number of a graph G is the minimum number of edges in a graph H such that every 2-edge-coloring of H yields a monochromatic copy of G. Size-Ramsey numbers of graphs have been studied for almost 40 years with particular focus on the case of trees and bounded degree graphs. We initiate the study of size-Ramsey numbers for k-uniform hypergraphs. Analogous to the graph case, we consider the size-Ramsey number of cliques, paths, trees, and bounded degree hypergraphs. Our results suggest that size-Ramsey numbers for hypergraphs are extremely difficult to determine, and many open problems remain.