Turán's theorem in sparse random graphs

2003 ◽  
Vol 23 (3) ◽  
pp. 225-234 ◽  
Author(s):  
Tibor Szabó ◽  
Van H. Vu
Keyword(s):  
Random Graphs ◽  
Turan's Theorem ◽  
Turán’S Theorem

scholarly journals Turán's theorem for pseudo-random graphs

2007 ◽  
Vol 114 (4) ◽  
pp. 631-657 ◽  
Author(s):  
Yoshiharu Kohayakawa ◽  
Vojtěch Rödl ◽  
Mathias Schacht ◽  
Papa Sissokho ◽  
Jozef Skokan
Keyword(s):  
Random Graphs ◽  
Turan's Theorem ◽  
Turán’S Theorem

scholarly journals On the Turán Properties of Infinite Graphs

10.37236/771 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Andrzej Dudek ◽  
Vojtěch Rödl
Keyword(s):  
Infinite Graph ◽  
Infinite Graphs ◽  
The Other ◽  
Other Hand ◽  
Turan's Theorem ◽  
Vertex Set ◽  
Turán’S Theorem ◽  
Positive Integers

Let $G^{(\infty)}$ be an infinite graph with the vertex set corresponding to the set of positive integers ${\Bbb N}$. Denote by $G^{(l)}$ a subgraph of $G^{(\infty)}$ which is spanned by the vertices $\{1,\dots,l\}$. As a possible extension of Turán's theorem to infinite graphs, in this paper we will examine how large $\liminf_{l\rightarrow \infty} {|E(G^{(l)})|\over l^2}$ can be for an infinite graph $G^{(\infty)}$, which does not contain an increasing path $I_k$ with $k+1$ vertices. We will show that for sufficiently large $k$ there are $I_k$–free infinite graphs with ${1\over 4}+{1\over 200} < \liminf_{l\rightarrow \infty} {|E(G^{(l)})|\over l^2}$. This disproves a conjecture of J. Czipszer, P. Erdős and A. Hajnal. On the other hand, we will show that $\liminf_{l\rightarrow \infty} {|E(G^{(l)})|\over l^2}\le{1\over 3}$ for any $k$ and such $G^{(\infty)}$.

scholarly journals Turán’s Theorem for the Fano Plane

COMBINATORICA ◽  
2019 ◽  
Vol 39 (5) ◽  
pp. 961-982 ◽  
Author(s):  
Louis Bellmann ◽  
Christian Reiher
Keyword(s):  
Fano Plane ◽  
Turan's Theorem ◽  
Turán’S Theorem

A note on Turán’s theorem

2019 ◽  
Vol 361 ◽  
pp. 13-14
Author(s):  
Long-Tu Yuan
Keyword(s):  
Turan's Theorem ◽  
Turán’S Theorem

On ordered set systems and some conjectures related to the erdös–ko–rado theorem and turán's theorem

Mathematika ◽  
1981 ◽  
Vol 28 (1) ◽  
pp. 54-66 ◽  
Author(s):  
A. J. W. Hilton
Keyword(s):  
Ordered Set ◽  
Set Systems ◽  
Turan's Theorem ◽  
Turán’S Theorem

A Short Proof of Turán's Theorem

1999 ◽  
Vol 106 (3) ◽  
pp. 257-258
Author(s):  
William Staton
Keyword(s):  
Short Proof ◽  
Turan's Theorem ◽  
Turán’S Theorem

scholarly journals Large dense neighbourhoods and turán's theorem

1983 ◽  
Vol 34 (1) ◽  
pp. 109-111 ◽  
Author(s):  
J.A Bondy
Keyword(s):  
Turan's Theorem ◽  
Turán’S Theorem

scholarly journals Turán's theorem for k-graphs

1972 ◽  
Vol 2 (2) ◽  
pp. 183-186 ◽  
Author(s):  
Joel Spencer
Keyword(s):  
Turan's Theorem ◽  
Turán’S Theorem

scholarly journals Turán's Theorem and Maximal Degrees

1999 ◽  
Vol 75 (1) ◽  
pp. 160-164 ◽  
Author(s):  
Béla Bollobás
Keyword(s):  
Turan's Theorem ◽  
Turán’S Theorem

scholarly journals Dense neighbourhoods and Turán's theorem

1981 ◽  
Vol 31 (1) ◽  
pp. 111-114 ◽  
Author(s):  
Béla Bollobás ◽  
Andrew Thomason
Keyword(s):  
Turan's Theorem ◽  
Turán’S Theorem
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