The Turán Number for 4 · Sℓ1 - Li Sha-Sha; Yin Jian-Hua; Li Jia-Yun (Discussiones Mathematicae Graph Theory, 2022)
The Turán number of a graph H, denoted by ex(n, H), is the maximum number of edges of an n-vertex simple graph having no H as a subgraph. Let Sℓ denote the star on ℓ + 1 vertices, and let k · Sℓ denote k disjoint copies of Sℓ. Erdős and Gallai determined the value ex(n, k · S1) for all positive integers k and n. Yuan and Zhang determined the value ex(n, k · S2) and characterized all extremal graphs for all positive integers k and n. Recently, Lan et al. determined the value ex(n, 2 · S3) for all positive integers n, and Li and Yin determined the values ex(n, k · Sℓ) for k = 2, 3 and all positive integers ℓ and n. In this paper, we further determine the value ex(n, 4 · Sℓ) for all positive integers ℓ and almost all n, improving one of the results of Lidický et al.