Some new results on the Turán number of star forests

Abstract

Let ex(n,G)=max{e(H)|Hisagraphwith|V(H)|=nandHcontainsnoG}, the Turán number of a graph G, where e(H)=|E(H)|. We determine ex(n,Sℓ1∪Sℓ2) for ℓ2≥3,ℓ1≥2ℓ2+2 and n≥2ℓ1+2ℓ2, where Sℓ is the star of order ℓ+1 and ∪ is the disjoint union. Moreover, we also determine ex(n,Sℓ1∪Sℓ2∪Sℓ3) for ℓ1≥ℓ2≥ℓ3≥1 and n≥max{M1,M2}, where both M1 and M2 are two parameters only depending on ℓ1,ℓ2 and ℓ3. This improves the corresponding results due to Lidický et al. (2013).