Geodesic
The Turán number of spanning star forests
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 2, pp. 303-312

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Let ℱ be a family of graphs. The Turán number of ℱ, denoted by ex(n, ℱ), is the maximum number of edges in a graph with n vertices which does not contain any subgraph isomorphic to some graph in ℱ. A star forest is a forest whose connected components are all stars and isolated vertices. Motivated by the results of Wang, Yang and Ning about the spanning Turán number of linear forests [J. Wang and W. Yang, The Turán number for spanning linear forests, Discrete Appl. Math. 254 (2019) 291–294; B. Ning and J. Wang, The formula for Turán number of spanning linear forests, Discrete Math. 343 (2020) #111924]. In this paper, let 𝒮_n, k be the set of all star forests with n vertices and k edges. We prove that when 1≤ k≤ n-1, ex(n,𝒮_n, k)= ⌊k^2-1/2⌋.
Keywords: spanning Turán problem, star forests, Loebl-Komlós-Sós type problems 
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Zhang, Lin-Peng; Wang, Ligong; Zhou, Jiale. The Turán number of spanning star forests. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 2, pp. 303-312. http://geodesic.mathdoc.fr/item/DMGT_2023_43_2_a0/