Turán's problem and Ramsey numbers for trees

Zhi-Hong Sun, Lin-Lin Wang, and Yi-Li Wu. "Turán's problem and Ramsey numbers for trees." Colloquium Mathematicae 139.2 (2015): 273-298. <http://eudml.org/doc/284134>.

@article{Zhi2015,
abstract = {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.},
author = {Zhi-Hong Sun, Lin-Lin Wang, Yi-Li Wu},
journal = {Colloquium Mathematicae},
keywords = {Ramsey number; Turán’s problem},
language = {eng},
number = {2},
pages = {273-298},
title = {Turán's problem and Ramsey numbers for trees},
url = {http://eudml.org/doc/284134},
volume = {139},
year = {2015},
}

TY - JOUR
AU - Zhi-Hong Sun
AU - Lin-Lin Wang
AU - Yi-Li Wu
TI - Turán's problem and Ramsey numbers for trees
JO - Colloquium Mathematicae
PY - 2015
VL - 139
IS - 2
SP - 273
EP - 298
AB - 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.
LA - eng
KW - Ramsey number; Turán’s problem
UR - http://eudml.org/doc/284134
ER -