We use random sampling as a tool for solving undirected graph problems. We show that the sparse graph, or skeleton, that arises when we randomly sample a graph's edges will accurately approximate the ...

References [1] Measures on the square as sparse graph limits. Journal of Combinatorial Theory Series B (2019). [2] Limits of dense graph sequences. Journal of Combinatorial Theory Series B (2006).

We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates for the mean and variance of the ...