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On the maximum number of common neighbours in dense random regular graphs
Mikhail Isaev, Maksim Zhukovskii
We derive the distribution of the maximum number of common neighbours of a pair of vertices in a dense random regular graph.The proof involves two important steps. One step is to e…
Cumulant expansion for counting Eulerian orientations
Mikhail Isaev, Brendan D. McKay, Rui-Ray Zhang
An Eulerian orientation is an orientation of the edges of a graph such that every vertex is balanced: its in-degree equals its out-degree. Counting Eulerian orientations correspond…
Sprinkling with random regular graphs
Mikhail Isaev, Brendan D. McKay, Angus Southwell +1
We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the same vertex set is asymptotically equivalent to a random regular graph of the com…