Bipartite Turán Problems for Ordered Graphs Abhishek Methuku, István Tomon

COMBINATORICA ◽  
2022 ◽  
Author(s):  
Abhishek Methuku ◽  
István Tomon
Keyword(s):  
Turan Problems ◽  
Ordered Graphs

On a Two-Sided Turán Problem

10.37236/1735 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Dhruv Mubayi ◽  
Yi Zhao
Keyword(s):  
Minimum Size ◽  
Turan Problem ◽  
Turan Problems ◽  
Turán Problem ◽  
Positive Integers

Given positive integers $n,k,t$, with $2 \le k\le n$, and $t < 2^k$, let $m(n,k,t)$ be the minimum size of a family ${\cal F}$ of nonempty subsets of $[n]$ such that every $k$-set in $[n]$ contains at least $t$ sets from ${\cal F}$, and every $(k-1)$-set in $[n]$ contains at most $t-1$ sets from ${\cal F}$. Sloan et al. determined $m(n, 3, 2)$ and Füredi et al. studied $m(n, 4, t)$ for $t=2, 3$. We consider $m(n, 3, t)$ and $m(n, 4, t)$ for all the remaining values of $t$ and obtain their exact values except for $k=4$ and $t= 6, 7, 11, 12$. For example, we prove that $ m(n, 4, 5) = {n \choose 2}-17$ for $n\ge 160$. The values of $m(n, 4, t)$ for $t=7,11,12$ are determined in terms of well-known (and open) Turán problems for graphs and hypergraphs. We also obtain bounds of $m(n, 4, 6)$ that differ by absolute constants.

Generalizing Vertex Pancyclic and $$k$$ k -ordered Graphs

2014 ◽  
Vol 31 (5) ◽  
pp. 1539-1554
Author(s):  
Ruijuan Li ◽  
Xinhong Zhang ◽  
Qiaoping Guo
Keyword(s):  
Ordered Graphs

Relative Turán Problems for Uniform Hypergraphs

2021 ◽  
Vol 35 (3) ◽  
pp. 2170-2191
Author(s):  
Sam Spiro ◽  
Jacques Verstraëte
Keyword(s):  
Uniform Hypergraphs ◽  
Turan Problems

scholarly journals On ordered graphs and graph orderings

1994 ◽  
Vol 51 (1-2) ◽  
pp. 113-116 ◽  
Author(s):  
Jaroslav Nešetřil
Keyword(s):  
Ordered Graphs

A Fan-type result on k-ordered graphs

2010 ◽  
Vol 110 (16) ◽  
pp. 651-654 ◽  
Author(s):  
Ruijuan Li
Keyword(s):  
Type Result ◽  
Ordered Graphs

scholarly journals On Growth Rates of Permutations, Set Partitions, Ordered Graphs and Other Objects

10.37236/799 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Martin Klazar
Keyword(s):  
Growth Rates ◽  
Fibonacci Numbers ◽  
Complete Graphs ◽  
Linear Orders ◽  
Set Partitions ◽  
Ordered Graphs ◽  
Containment Order ◽  
Hereditary Properties ◽  
Finite Linear ◽  
Lower Ideal

For classes ${\cal O}$ of structures on finite linear orders (permutations, ordered graphs etc.) endowed with containment order $\preceq$ (containment of permutations, subgraph relation etc.), we investigate restrictions on the function $f(n)$ counting objects with size $n$ in a lower ideal in $({\cal O},\preceq)$. We present a framework of edge $P$-colored complete graphs $({\cal C}(P),\preceq)$ which includes many of these situations, and we prove for it two such restrictions (jumps in growth): $f(n)$ is eventually constant or $f(n)\ge n$ for all $n\ge 1$; $f(n)\le n^c$ for all $n\ge 1$ for a constant $c>0$ or $f(n)\ge F_n$ for all $n\ge 1$, $F_n$ being the Fibonacci numbers. This generalizes a fragment of a more detailed theorem of Balogh, Bollobás and Morris on hereditary properties of ordered graphs.

scholarly journals Rational exponents for hypergraph Turan problems

2019 ◽  
Vol 10 (1) ◽  
pp. 61-86
Author(s):  
Matthew Fitch
Keyword(s):  
Turan Problems

scholarly journals Counting ordered graphs that avoid certain subgraphs

2016 ◽  
Vol 339 (7) ◽  
pp. 1871-1877
Author(s):  
László Ozsvárt
Keyword(s):  
Ordered Graphs
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