0-1 matrices whose squares have bounded entries

Lyu, Zhenhua

doi:10.1016/j.laa.2020.07.035

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

2022

Publication Types

Select...

Article2

Relationship

Self Cite1

Independent1

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the last decade, Problem 1 for the case t = 1 has been completely solved by Wu [12], by Huang and Zhan [8], by Huang, Lyu and Qiao [7], by Lyu [11], and by Huang and Lyu [6]. For the general cases of Problem 1, the case k = 2 has been studied in [9], and the case for k ≥ n − 1 ≥ 6t + 1 has been solved in [5].…”

Section: Introductionmentioning

confidence: 99%

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

Lyu

2021

J Comb Optim

Self Cite

View full text Add to dashboard Cite

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 2t + 9/4 + 1/2 + 3}. Based on this result, we may determine the maximum numbers and the extremal digraphs for k ≥ max{2t + 1, 2 2t + 9/4 + 1/2 + 3} and n is sufficiently large, which generalises the existing results. A conjecture is also presented.

show abstract