# On the maximum density of fixed strongly connected subtournaments

@article{Parente2015OnTM, title={On the maximum density of fixed strongly connected subtournaments}, author={Roberto F. Parente and Cristiane M. Sato}, journal={ArXiv}, year={2015}, volume={abs/1505.05200} }

We study the density of fixed strongly connected subtournaments on 5 vertices in large tournaments. We determine the maximum density asymptotically for five tournaments as well as unique extremal sequences for each tournament. As a byproduct we also characterize tournaments that are recursive blow-ups of a 3-cycle as tournaments that avoid three specific tournaments of size 5.

## 14 Citations

### Inducibility of 4-vertex tournaments

- Mathematics
- 2021

We determine the inducibility of all tournaments with at most 4 vertices together with the extremal constructions. The 4-vertex tournament containing an oriented C 3 and one source vertex has a…

### A ug 2 02 0 Cycles of a given length in tournaments ∗ ( Dedicated to the memory of Robin Thomas )

- Mathematics
- 2020

We study the asymptotic behavior of the maximum number of directed cycles of a given length in a tournament: let c(l) be the limit of the ratio of the maximum number of cycles of length l in an…

### Quasirandom forcing orientations of cycles

- Mathematics
- 2022

An oriented graph H is quasirandom-forcing if the limit (homomorphic) density of H in a sequence of tournaments is 2 −k H k if and only if the sequence is quasirandom. We study generalizations of the…

### Tournament Quasirandomness from Local Counting

- MathematicsComb.
- 2021

This paper investigates the relationship between quasirandomness of T and the count of a single h -vertex tournament H in T and proves that a constant proportion of all tournaments are not locally forcing.

### Tournament Quasirandomness from Local Counting

- MathematicsCombinatorica
- 2021

A well-known theorem of Chung and Graham states that if h ≥ 4 then a tournament T is quasirandom if and only if T contains each h-vertex tournament the ‘correct number’ of times as a subtournament.…

### Mathematics 11-9-2018 Inducibility of directed paths

- Mathematics
- 2018

A long standing open problem in extremal graph theory is to describe all graphs that maximize the number of induced copies of a path on four vertices. The character of the problem changes in the…

### A note on directed analogues of the Sidorenko and forcing conjectures

- Mathematics
- 2022

. We study analogues of Sidorenko’s conjecture and the forcing conjecture in oriented graphs, showing that natural variants of these conjectures in directed graphs are equivalent to the asymmetric,…

## References

SHOWING 1-10 OF 44 REFERENCES

### On the Density of Transitive Tournaments

- MathematicsJ. Graph Theory
- 2017

We prove that for every fixed k, the number of occurrences of the transitive tournament Trk of order k in a tournament Tn on n vertices is asymptotically minimized when Tn is random. In the opposite…

### A Note on Even Cycles and Quasirandom Tournaments

- MathematicsJ. Graph Theory
- 2013

It is shown that for every fixed even integer k ≥ 4, if close to half of the k-cycles in a tournament T are even, then T must be quasi-random.

### Quasi-random tournaments

- MathematicsJ. Graph Theory
- 1991

A large class of tournament properties, all of which are shared by almost all random tournaments, are introduced, which have the property that tournaments possessing any one of the properties must of necessity possess them all.

### GRAPH LIMITS AND EXCHANGEABLE RANDOM GRAPHS

- Mathematics
- 2008

We develop a clear connection between de Finetti’s theorem for exchangeable arrays (work of Aldous–Hoover–Kallenberg) and the emerging area of graph limits (work of Lovász and many coauthors). Along…

### The Maximum Number of Strongly Connected Subtournaments*

- MathematicsCanadian Mathematical Bulletin
- 1965

In the ranking of a collection of p objects by the method of paired comparisons, a measure of consistency is provided by the relative number of transitive (or consistent) triples and cyclic (or…

### Some results in extremal combinatorics

- Mathematics
- 2011

In Chapter 1 we determine the minimal density of triangles in a tripartite graph with prescribed edge densities. This extends work of Bondy, Shen, Thomasse and Thomassen characterizing those edge…

### Quasi-Random Hypergraphs

- MathematicsRandom Struct. Algorithms
- 1990

A large equivalence class of properties shared by most hypergraphs, including so-called random hyper graphs, are described, which shows that many global properties of hyperGraphs are actually consequences of simple local conditions.

### Quasi‐Random Oriented Graphs

- MathematicsJ. Graph Theory
- 2013

The main theorem extends to the case of a general underlying graph G, the main result of [3] which corresponds to the Case that G is complete, and shows that a number of conditions on oriented graphs are equivalent.