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Mathematics > Combinatorics

arXiv:2503.03487 (math)
[Submitted on 5 Mar 2025 (v1) , last revised 29 Jun 2025 (this version, v3)]

Title: The planar Turan number of double star S_(3,5)

Title: 平面图的Turán数双星S_(3,5)

Authors:Dandan Liu, Shoujun Xu
Abstract: Given a graph H and a positive integer n, the planar Turan number of H, denoted by exp(n, H), is the maximum number of edges in an n-vertex H-free planar graph.D.Ghosh, et al.initiated the topic of double stars S_(k,l). Recently Xu et al.[AIMS Mathematics, 2025, 10(1): 1628-1644.] mentioned that exp(n, S_(3,5)) is still unknown.In this paper, we first establish that the planar Turan number S_(3,5) satisfies exp(n, S_(3,5)) <= 23n/8 - 9/2 for all n >= 2. The upper bound is tight for n = 12.
Subjects: Combinatorics (math.CO)
Cite as: arXiv:2503.03487 [math.CO]
  (or arXiv:2503.03487v3 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.2503.03487

Submission history

From: Dandan Liu [view email]
[v1] Wed, 5 Mar 2025 13:25:04 UTC (2,973 KB)
[v2] Mon, 23 Jun 2025 15:30:00 UTC (3,884 KB)
[v3] Sun, 29 Jun 2025 10:08:27 UTC (6,779 KB)
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