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The Maximum Number of Paths of Length Three in a Planar Graph

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Extended Abstracts EuroComb 2021

Part of the book series: Trends in Mathematics ((RPCRMB,volume 14))

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Abstract

Let f(nH) denote the maximum number of copies of H possible in an n-vertex planar graph. The function f(nH) has been determined when H is a cycle of length 3 or 4 by Hakimi and Schmeichel and when H is a complete bipartite graph with smaller part of size 1 or 2 by Alon and Caro. We determine f(nH) exactly in the case when H is a path of length 3.

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Acknowledgements

The research of the first, third and fifth authors is partially supported by the National Research, Development and Innovation Office – NKFIH, grant K 116769, K 132696 and SNN 117879. The research of the third author is partially supported by the Shota Rustaveli National Science Foundation of Georgia SRNSFG, grant number DI-18-118. The research of the fourth author is supported by the Institute for Basic Science (IBS-R029-C1).

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Győri, E., Paulos, A., Salia, N., Tompkins, C., Zamora, O. (2021). The Maximum Number of Paths of Length Three in a Planar Graph. In: Nešetřil, J., Perarnau, G., Rué, J., Serra, O. (eds) Extended Abstracts EuroComb 2021. Trends in Mathematics(), vol 14. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-83823-2_41

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