A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections. “It’s a bit of a surprise, at least for me, that such a combination ...

Graph limit theory provides a rigorous framework for analysing sequences of large graphs by representing them as continuous objects known as graphons – symmetric measurable functions on the unit ...

For any α ∈ (0, 1) and any nα ≤ d ≤ n/2, we show that λ(G) ≤ Cα√d with probability at least 1− 1 n , where G is the uniform random undirected d-regular graph on n vertices, λ(G) denotes its second ...