  Vertex bisection is a graph partitioning problem in which the aim is to find
a partition into two equal parts that minimizes the number of vertices in one
partition set that have a neighbor in the other set. We are interested in
giving upper bounds on the vertex bisection width of random $d$-regular graphs
for constant values of $d$. Our approach is based on analyzing a greedy
algorithm by using the Differential Equations Method. In this way, we obtain
the first known upper bounds for the vertex bisection width in random regular
graphs. The results are compared with experimental ones and with lower bounds
obtained by Kolesnik and Wormald, (Lower Bounds for the Isoperimetric Numbers
of Random Regular Graphs, SIAM J. on Disc. Math. 28(1), 553-575, 2014).
