The Turan number of k•Sl

The Turan 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 S-l denote the star on l + 1 vertices, and let k center dot S-l denote the disjoint union of k copies of S-l. Erdos and Gallai determined ex(n, k center dot S-1) for all positive integers k and n. Yuan and Zhang determined ex(n, k center dot S-2) and characterized all extremal graphs for all positive integers k and n. Lidicky et al. determined ex(n, k center dot S-l) for k, l >= 1 and n sufficiently large. Lan et al. determined ex(n, k center dot S-l) for k >= 2, l >= 3 and n >= k(l(2) + l + 1) - 2 (l - 3). In this paper, we completely determine ex(n, k center dot S-l) for all positive integers k, B and n. (c) 2021 Elsevier B.V. All rights reserved.