The planar Turán number of a graph G, denoted exP (n, G), is the maximum number of
edges in a planar graph on n vertices without containing G as a subgraph. Given a positive …

For a planar graph HH, let NP (n, H) N_P(n,H) denote the maximum number of copies of HH
in an nn‐vertex planar graph. In this paper, we prove that NP (n, P 7)~ 4 27 n 4 N_P(n,P_7) …

Given a fixed graph H that embeds in a surface, what is the maximum number of copies of H
in an n-vertex graph G that embeds in? We show that the answer is, where f (H) is a graph …

In a generalized Tur\'an problem, we are given graphs $ H $ and $ F $ and seek to maximize
the number of copies of $ H $ in an $ F $-free graph of order $ n $. We consider generalized …

What is the maximum number of copies of a fixed forest T in an n-vertex graph in a graph
class as? We answer this question for a variety of sparse graph classes. In particular, we …

The maximum number of paths of length four in a planar graph - ScienceDirect Skip to main
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Let f (n, H) denote the maximum number of copies of H possible in an n-vertex planar graph.
The function f (n, H) has been determined when H is a cycle of length 3 or 4 by Hakimi and …

For a fixed graph $ H $ and for arbitrarily large host graphs $ G $, the number of
homomorphisms from $ H $ to $ G $ and the number of subgraphs isomorphic to $ H …

Let f (n, H) f(n,H) denote the maximum number of copies of HH possible in an nn‐vertex
planar graph. The function f (n, H) f(n,H) has been determined when HH is a cycle of length …

For a fixed planar graph H, let NP (n, H) denote the maximum number of copies of H in an n-
vertex planar graph. In the case when H is a cycle, the asymptotic value of NP (n, C m) is …