Planar Turán number of double star $ S_{3, 4} $

Xin Xu; Xu Zhang; Jiawei Shao; Xin Xu; Xu Zhang; Jiawei Shao

doi:10.3934/math.2025075

AIMS Mathematics

2025, Volume 10, Issue 1: 1628-1644. doi: 10.3934/math.2025075

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Research article

Planar Turán number of double star $ S_{3, 4} $

College of Science, North China University of Technology, Beijing, China

Received: 21 December 2024 Revised: 15 January 2025 Accepted: 20 January 2025 Published: 23 January 2025
MSC : 05C35

Planar Turán number, denoted by $ \mathrm{ex}_{\mathcal{P}}(n, H) $, is the maximum number of edges in an $ n $-vertex planar graph which does not contain $ H $ as a subgraph. Ghosh, Győri, Paulos and Xiao initiated the topic of the planar Turán number for double stars. There were two double stars $ S_{3, 4} $ and $ S_{3, 5} $ that remained unknown. In this paper, we give the exact value of $ \mathrm{ex}_{\mathcal{P}}(n, S_{3, 4}) $.
- Turán-type problem,
- planar graph,
- double star,
- extremal graphs
Citation: Xin Xu, Xu Zhang, Jiawei Shao. Planar Turán number of double star $ S_{3, 4} $[J]. AIMS Mathematics, 2025, 10(1): 1628-1644. doi: 10.3934/math.2025075

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Abstract

Planar Turán number, denoted by $ \mathrm{ex}_{\mathcal{P}}(n, H) $, is the maximum number of edges in an $ n $-vertex planar graph which does not contain $ H $ as a subgraph. Ghosh, Győri, Paulos and Xiao initiated the topic of the planar Turán number for double stars. There were two double stars $ S_{3, 4} $ and $ S_{3, 5} $ that remained unknown. In this paper, we give the exact value of $ \mathrm{ex}_{\mathcal{P}}(n, S_{3, 4}) $.

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