On Turán number for Sℓ1∪Sℓ2

摘要

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.