Geodesic
Generalized planar Turán numbers
Ervin Győri ; Addisu Paulos ; Nika Salia ; Casey Tompkins ; Oscar Zamora1
1Central European University/ Universidad de Costa Rica
The electronic journal of combinatorics, Tome 28 (2021) no. 4
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In a generalized Turán problem, we are given graphs $H$ and $F$ and seek to maximize the number of copies of $H$ in an $n$-vertex graph not containing $F$ as a subgraph. We consider generalized Turán problems where the host graph is planar. In particular, we obtain the order of magnitude of the maximum number of copies of a fixed tree in a planar graph containing no even cycle of length at most $2\ell$, for all $\ell$, $\ell \geqslant 1$. We also determine the order of magnitude of the maximum number of cycles of a given length in a planar $C_4$-free graph. An exact result is given for the maximum number of $5$-cycles in a $C_4$-free planar graph. Multiple conjectures are also introduced.
DOI : 10.37236/9603
Classification : 05C30, 05C10, 05C35, 05C38, 05C12
Mots-clés : Turán problem, maximum number of cycles of a given length

Ervin Győri    ; Addisu Paulos    ; Nika Salia    ; Casey Tompkins    ; Oscar Zamora  1

1 Central European University/ Universidad de Costa Rica 
@article{10_37236_9603,
     author = {Ervin Gy\H{o}ri and Addisu  Paulos and Nika Salia and Casey  Tompkins and Oscar Zamora},
     title = {Generalized planar {Tur\'an} numbers},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {4},
     doi = {10.37236/9603},
     zbl = {1478.05074},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/9603/}
}
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Ervin Győri; Addisu  Paulos; Nika Salia; Casey  Tompkins; Oscar Zamora. Generalized planar Turán numbers. The electronic journal of combinatorics, Tome 28 (2021) no. 4. doi: 10.37236/9603

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