Extremal C4-Free/C5-Free Planar Graphs

@article{Dowden2016ExtremalCP,
  title={Extremal C4-Free/C5-Free Planar Graphs},
  author={Chris Dowden},
  journal={Journal of Graph Theory},
  year={2016},
  volume={83},
  pages={213-230}
}
We study the topic of “extremal” planar graphs, defining exP (n, H ) to be the maximum number of edges possible in a planar graph on n vertices that does not contain a given graph H as a subgraph. In particular, we examine the case when H is a small cycle, obtaining exP (n,C4) ≤ 15 7 (n − 2) for all n ≥ 4 and exP (n,C5) ≤ 12n−33 5 for all n ≥ 11, and showing that both of these bounds are tight. C © 2015 Wiley Periodicals, Inc. J. Graph Theory 00: 1–18, 2015 

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