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math.CO2023
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…
math.CO2023
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…