… Finally we consider the case where T is a bipartite graph and H is a tree. For a tree H, any …
H-free graph G = ( V , E ) on n vertices contains less than n t − ϵ copies of T for some ϵ = ϵ ( T …

… number of copies of T in an H-free graph on n vertices. When T = K2 is a single edge, ex(n,T,H…
Finally we consider the case where T is a bipartite graph and H is a tree. For a tree H, any …

… We say that a graph G is H-free if G does not contain H as a (… Denote by fn(H) the number of
labeled H-free graphs on a … random graph G(n, p) has many uniformly distributed copies of H…

… A graph is called H-free if it contains no copy of H. Denote by fn(H) the number of (labeled)
H-free graphs … We say that a graph G is H-free, if G does not contain H as a (not necessarily …

… independent sets in Vi corresponding to vertices of A from the previous step, along with Vj
, we can find an appropriate copy of the graph induced by A and B to complete our copy of H. …

… ABSTRACT: Given a graph H, a random maximal H-free graph … First assign to each edge of
the complete graph on n vertices … a graph F, we write ZF for the number of copies of F in Gn p. …

… In particular, we show that the graph produced by the H-free process is very similar to the …
Theorem 1.6 Suppose is an H-free graph and write X (i) for the number of labelled copies of in …

… ) we can still take whp an H-free subgraph of G(n, p) that contains most of the copies of Km:
… whp the cluster graph is H-free. Assume that there is a copy of H in the cluster graph, induced …

… :rsa20488-math-0077 vertices and no induced copy of H has a homogeneous set of size
urn:… of copies of H in G must be close to that in a typical graph on |V (G)| vertices and the copies …

… of maximizing the number of copies of T in an H-free graph, for a pair of graphs T and H. …
of magnitude for some classes of graphs H, we focus on the case when T and H are paths, …