Imagine 100 dots scattered in front of you. In a haphazard variation on connect-the-dots, start drawing lines between the points. How many lines can you draw without producing a triangle? A square? An ...

Recent advances in the study of automorphism groups within graph theory have yielded significant theoretical and applied insights. At its core, the interplay between the algebraic structure of groups ...

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 ...