# A note on extremal digraphs containing at most $t$ walks of length $k$ with the same endpoints

@inproceedings{Lyu2021ANO, title={A note on extremal digraphs containing at most \$t\$ walks of length \$k\$ with the same endpoints}, author={Zhenhua Lyu}, year={2021} }

Let n, k, t be positive integers. What is the maximum number of arcs in a digraph on n vertices in which there are at most t distinct walks of length k with the same endpoints? In this paper, we prove that the maximum number is equal to n(n− 1)/2 and the extremal digraph are the transitive tournaments when k ≥ n− 1 ≥ max{2t+ 1, 2 ⌈

## References

SHOWING 1-10 OF 16 REFERENCES

A Turán problem on digraphs avoiding distinct walks of a given length with the same endpoints

- Computer Science, MathematicsDiscret. Math.
- 2019

The maximum size of digraphs of order n that avoid distinct walks of length k with the same endpoints is determined and the extremalDigraphs attaining this maximum number when k ≥ 5 are characterized.

Extremal digraphs avoiding distinct walks of length 4 with the same endpoints

- Mathematics
- 2020

In this paper, we determine the maximum size of digraphs on n vertices in which there are no two distinct walks of length 3 with the same initial vertex and the same terminal vertex. The digraphs…

Digraphs that have at most one walk of a given length with the same endpoints

- Computer Science, MathematicsDiscret. Math.
- 2011

It is proved that if n>=5 and k>=n-1 then @q(n,k)=n( n-1)/2 and this maximum number is attained at D if and only if D is a transitive tournament.

Extremal problems for directed graphs

- Mathematics
- 1973

Abstract We consider directed graphs without loops and multiple edges, where the exclusion of multiple edges means that two vertices cannot be joined by two edges of the same orientation. Let L 1 ,…,…

0–1 matrices whose k-th powers have bounded entries

- Mathematics
- 2020

ABSTRACT Let be the set of 0–1 matrices of order n such that each entry of the k-th powers of these matrices is bounded by t. Let be the maximum number of nonzero entries of a matrix in . Given any…

Graph Theory with Applications

- Computer Science
- 1977

The burgeoning of Graph Theory was first aware when I studied the 1940 paper of Brooks, Smith, Stone and Tutte in the Duke Mathematical Journal, ostensibly on squared rectangles, all in the Quest of the Perfect Square.

0-1 matrices whose squares have bounded entries

- Mathematics
- 2020

Abstract Let Γ ( n , k , t ) be the set of 0-1 matrices of order n such that each entry of the k-th powers of these matrices is bounded by t. Let γ ( n , k , t ) be the maximum number of nonzero…

On the 0–1 matrices whose squares are 0–1 matrices

- Mathematics
- 2010

Abstract We study the 0–1 matrices whose squares are still 0–1 matrices and determine the maximal number of ones in such a matrix. The maximizing matrices are also specified. This solves a special…

Digraphs that contain at most t distinct walks of a given length with the same endpoints

- Computer ScienceJ. Comb. Optim.
- 2021

Extremal multigraph and digraph problems

- Paul Erdős and his mathematics, II
- 1999