… the topic of “extremal” planar graphs, that is, how many edges can an H-free planar graph on
n … We define exP (n, H) to be the maximum number of edges in an H-free planar graph on n …

… Let us say that a graph is H-free if it does not contain H as a subgraph (whether induced or
… -0015 denote the maximum number of edges possible in a planar H-free graph on n vertices. …

… restrict the graph classes to planar graphs, that is… H-free planar graphs on n vertices.
Obviously, we have \(\mathrm{{ex}}_{_{\mathcal {P}}}(n,H)=3n-6\) if the graph H is not a planar graph…

… to study the spectral extremal problems on planar graphs, we … the spectral extremal graph
among Cℓ-free graphs for odd ℓ … the spectral extremal graphs among Cℓ-free planar graphs. …

… In particular we show that a path-pairable planar graph must have a vertex of linear degree.
… a maximal H-free graph on n vertices. We say that a graph is H-saturated if it is H-free but the …

… We now turn to b3 = 1 which already seems to be a very interesting special case that is related
to an open question in extremal graph theory (see Problem 7.3 in Section 7). Here (3) and …

… We now turn to b3 = 1 which already seems to be a very interesting special case that is related
to an open question in extremal graph theory (see Problem 7.3 in Section 7). Here (3) and …

… H as a subgraph (known as H-free graphs). Caro and Yuster proposed the problem of …
of graphs including planar graphs (and its extensions) [14, 15, 21, 33, 35, 38], bipartite …

… 1 Planar Turán number of graphs How many edges can an H-free planar graph on n vertices
… We refer the reader to [9] for their construction of the extremal graphs for C5. Lan, Shi and …

… extremal problems have been considered where the host graph is taken to be a planar
graph… of H possible in an n-vertex planar graph containing no graph F ∈ F as a subgraph (we …