The Turán number of star forests

摘要

The Turán number of a graph H, denoted by ex(n, H), is the maximum number of edges in any graph on n vertices containing no H as a subgraph. Let Sℓ denote the star on ℓ+1 vertices and let k · Sℓ denote disjoint union of k copies of Sℓ. In this paper, for appropriately large n, we determine the Turán numbers for k · Sℓ and F, where F is a forest with components each of order 4, which improve the results of Lidický et al. (2013).