Induced planar Tur\'an numbers
Ervin Gy\H{o}ri, Hilal Hama Karim

TL;DR
This paper introduces the concept of induced planar Turán numbers, establishing bounds and exact values for specific forbidden induced subgraphs in planar graphs.
Contribution
It defines induced planar Turán numbers and determines sharp bounds and exact extremal values for certain small forbidden induced subgraphs.
Findings
Sharp upper bound for $F=\Theta_4$
Exact extremal values for paths $P_3$, $P_4$, and $P_5$
Introduces a new variation of Turán numbers in planar graphs
Abstract
The planar Tur\'a number of a graph is the maximum number of edges an -vertex -free planar graph can have. We study the case where is forbidden as an induced subgraph, thereby introducing the induced planar Tur\'a numbers. We will determine a sharp upper bound when is , a -cycle with a diagonal edge, and obtain exact extremal values in case is a path on vertices, for and .
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