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On Turán number for Sℓ1∪Sℓ2

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  • Li, Jia-Yun
  • Li, Sha-Sha
  • Yin, Jian-Hua

Abstract

The Turán number of a graph G, denoted by ex(n, G), is the maximum number of edges of an n-vertex simple graph having no G as a subgraph. Let Sℓ denote the star on ℓ+1 vertices. In this paper, we investigate to determine the Turán number for Sℓ1∪Sℓ2, where ℓ1 > ℓ2. We give a new lower bound on ex(n,Sℓ1∪Sℓ2). Moreover, if ℓ2+1≤ℓ1≤2ℓ2+1 (or if ℓ1 ≥ 3 and ℓ2=2), we determine the exact values ex(n,Sℓ1∪Sℓ2) for all positive integers n (or for almost all positive integers n), which improves two results of Lidický et al.

Suggested Citation

  • Li, Jia-Yun & Li, Sha-Sha & Yin, Jian-Hua, 2020. "On Turán number for Sℓ1∪Sℓ2," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    • Handle: RePEc:eee:apmaco:v:385:y:2020:i:c:s0096300320303623
    DOI: 10.1016/j.amc.2020.125400
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    References listed on IDEAS

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    1. Lan, Yongxin & Li, Tao & Shi, Yongtang & Tu, Jianhua, 2019. "The Turán number of star forests," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 270-274.
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