The expected node-independence number of random trees

Expected Number of Local Maxima of Some Gaussian Random Polnomials

expected number of local maxima of some gaussian random polnomials

On the independence number of random graphs

Expected Shape of Random Binary Search Trees

This entry contains proofs for the textbook results about the distributions of the height and internal path length of random binary search trees (BSTs), i. e. BSTs that are formed by taking an empty BST and inserting elements from a fixed set in random order. In particular, we prove a logarithmic upper bound on the expected height and the Θ(n log n) closed-form solution for the expected interna...

On subgraph number independence in trees

For finite graphs F and G, let Nr(G) denote the number of occurrences of F in G, i.e., the number of subgraphs of G which are isomorphic to F. I f g and c?? are families of graphs, it is natural to ask then whether or not the quantities NF(G), FE F, are linearly independent when G is restricted to Q. For example, if P = (K1, &} (where K, denotes the complete graph on n vertices) and 9 is the fa...