1 citations · 1 across the 12 of their papers we have counts for
13 papers
Jaeger-type orientations of random regular graphs
Catherine Greenhill, Mikhail Isaev, Charles Lewis
We consider -orientations, which are defined to be orientations of -regular graphs such that every vertex either has in-degree or out-degree . These generalise the ori…
Canonical labelling of random regular graphs
Mikhail Isaev, Tamás Makai, Brendan McKay +3
We prove that whenever and as , then with high probability for any non-trivial initial colouring, the colour refinement algorithm disti…
Sandwiching between random regular graphs and Erdős-Rényi graphs: configuration model and unions of perfect matchings
Pu Gao, Mikhail Isaev, Xavier Perez-Gimenez
We establish new couplings among several random graph and multigraph models related to the random regular graph , including the configuration model and unions of random per…
On Pauling's residual entropy estimate for regular graphs with growing degree
M. Hasheminezhad, M. Isaev, B. D. McKay +1
In 1935, Pauling proposed an estimate for the number of Eulerian orientations of a graph in the context of the theoretical behaviour of water ice. The logarithm of the number of Eu…
A tail bound for cumulant series for complex functions of independent random variables
Mikhail Isaev
We obtain explicit bounds on the truncation error of the cumulant series of a bounded complex function of a random vector with independent components. The bounds are based on multi…
Asymptotic enumeration of graph factors by cumulant expansion
Mikhail Isaev, Brendan D. McKay
Let be a dense graph with good expansion properties and not too close to being bipartite. Let be a graphical degree sequence. Under very weak conditions, we fin…
Enumeration of regular multipartite hypergraphs
Mikhail Isaev, Tamás Makai, Brendan D. McKay
We determine the asymptotic number of regular multipartite hypergraphs, also known as multidimensional binary contingency tables, for all values of the parameters.
Correlation between residual entropy and spanning tree entropy of ice-type models on graphs
Mikhail Isaev, Brendan D. McKay, Rui-Ray Zhang
The logarithm of the number of Eulerian orientations, normalised by the number of vertices, is known as the residual entropy in studies of ice-type models on graphs. The spanning t…
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…
Sandwiching random regular graphs between binomial random graphs
Pu Gao, Mikhail Isaev, Brendan McKay
Kim and Vu made the following conjecture (\textit{Advances in Mathematics}, 2004): if , then the random -regular graph can asymptotically almost s…
Exponential instability in the Gel'fand inverse problem on the energy intervals
Mikhail Isaev
We consider the Gel'fand inverse problem and continue studies of [Mandache,2001]. We show that the Mandache-type instability remains valid even in the case of Dirichlet-to-Neumann…