Corpus ID: 236777096

# Planar graphs with the maximum number of induced 4-cycles or 5-cycles

@inproceedings{Savery2021PlanarGW,
title={Planar graphs with the maximum number of induced 4-cycles or 5-cycles},
author={Michael Savery},
year={2021}
}
For large n we determine exactly the maximum numbers of induced C4 and C5 subgraphs that a planar graph on n vertices can contain. We show that K2,n−2 uniquely achieves this maximum in the C4 case, and we identify the graphs which achieve the maximum in the C5 case. This extends work in a paper by Hakimi and Schmeichel and a paper by Ghosh, Győri, Janzer, Paulos, Salia, and Zamora which together determine both maxima asymptotically.
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