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Turán's problem and Ramsey numbers for trees

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Sun Z.-H., Wang L.-L., Wu Y.-L.

Colloquium Mathematicum

2015

tom 139

nr 2

273-298

Let T¹ₙ = (V,E₁) and T²ₙ = (V,E₂) be the trees on n vertices with $V = {v₀,v₁,...,v_{n-1}}$, $E₁ = {v₀v₁,..., v₀v_{n-3},v_{n-4}v_{n-2},v_{n-3}v_{n-1}}$ and $E₂ = {v₀v₁,..., v₀v_{n-3},v_{n-3}v_{n-2},v_{n-3}v_{n-1}}$. For p ≥ n ≥ 5 we obtain explicit formulas for ex(p;T¹ₙ) and ex(p;T²ₙ), where ex(p;L) denotes the maximal number of edges in a graph of order p not containing L as a subgraph. Let r(G₁,G₂) be the Ramsey number of the two graphs G₁ and G₂. We also obtain some explicit formulas for $r(Tₘ,Tₙ^i)$, where i ∈ {1,2} and Tₘ is a tree on m vertices with Δ(Tₘ) ≤ m - 3.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Sun Z.-H.

1 Wang L.-L.

1 Wu Y.-L.

1 2015

Wyniki wyszukiwania

Turán's problem and Ramsey numbers for trees