A random 2-cell embedding of a connected graph G in some orientable surface is obtained
by choosing a random local rotation around each vertex. Under this setup, the number of …

A random two-cell embedding of a given graph is obtained by choosing a random local
rotation around every vertex. We analyse the expected number of faces of such an …

We show that for the product of two fixed point free conjugacy classes, the average number
of cycles is always very similar. Specifically, our main result is that for a randomly chosen …

Let G be a connected simple graph with minimum degree larger than 1. Let v (G), e (G)
denote the number of vertices and edges of G, respectively. We show that the average …

We are interested in the distribution of the number of faces across all the 2− cell embeddings
of a graph, which is equivalent to the distribution of genus by Euler's formula. In order to …

For some A, B⊆ Sn, determining the cycle structure of the multiset AB={a· b: a∈ A, b∈ B} is
a problem arising in several different areas of mathematics. When the sets of permutations A …

A random 2-cell embedding of a connected graph G in some orientable surface is obtained
by choosinga random local rotation around each vertex. Under this setup, the number of …

In this paper, we first generalize a theorem for counting the number of faces of an oriented
embedding of a graph that passing through a given cut-edge set [S. Stahl, Trans. Amer …

A random two-cell embedding of a given graph $ G $ is obtained by choosing a random
local rotation around every vertex. We analyse the expected number of faces of such an …