Let Tn denote the set of unrooted labeled trees of size n and let M be a particular (finite, unlabeled) tree. Assuming that every tree of Tn is equally likely, it is shown that the...
If G is a graph with vertex set [n] then A 2[n] is G-intersecting if for all A, B A either A B = or there exist a A and b B such that a G b. The question of how large a k-un...
For any partition of {1, 2, . . . , n} we define its increments Xi, 1 i n by Xi = 1 if i is the smallest element in the partition block that contains it, Xi = 0 otherwise. We pr...
We give results for the age dependent distribution of vertex degree and number of vertices of given degree in the undirected web-graph process, a discrete random graph process int...
The adaption of combinatorial duality to infinite graphs has been hampered by the fact that while cuts (or cocycles) can be infinite, cycles are finite. We show that these obstruc...