2 citations · 5 across the 9 of their papers we have counts for
4 papers · 1 filter
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…
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…
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…
Asymptotic linearity of binomial random hypergraphs via cluster expansion under graph-dependence
Rui-Ray Zhang
Let integer and integer . Define the binomial random -uniform hypergraph to be the -uniform graph on the vertex set such that each…