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Generalized planar turán numbers

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Title
Generalized planar turán numbers
Author(s)
Gyõri, Ervin; Salia, Nika; Paulos, Addisu; Casey Tompkins; Zamora, Oscar
Publication Date
2021-11-19
Journal
Electronic Journal of Combinatorics, v.28, no.4, pp.1 - 15
Publisher
Australian National University
Abstract
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 Turan 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£, for all £, £ ^ 1. We also determine the order of magnitude of the maximum number of cycles of a given length in a planar C4-free graph. An exact result is given for the maximum number of 5-cycles in a C4-free planar graph. Multiple conjectures are also introduced.
URI
https://pr.ibs.re.kr/handle/8788114/11020
DOI
10.37236/9603
ISSN
1077-8926
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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