Archdeacon and Grable () proved that the genus of the random graph G∈ Gn, p is almost
surely close to pn if p= p (n)(ln n) n−. In this paper we prove an analogous result for random …

We investigate the genus g (n, m) of the Erdős‐Rényi random graph G (n, m), providing a
thorough description of how this relates to the function m= m (n), and finding that there is …

The genus of the binomial random graph G(n,p) is well understood for a wide range of
p=p(n). Recently, the study of the genus of the random bipartite graph G(n_1,n_2,p), with …

We define a model of random graphs that the vertex set is partitioned in to constant number
of sets, and the edges inside each part and between every two parts are chosen randomly …

The main results of this paper provide a polynomial time algorithm for approximating the
logarithm of the number of maximal near perfect matchings in dense graphs. By dense we …

The question which planar graphs are 3-colorable is well investigated. Starting with
Heawood, who showed that a plane triangulation is 3-colorable if and only if all its vertices …