English

Extremal digraphs avoiding distinct walks of length 3 with the same endpoints

Combinatorics 2021-04-20 v1

Abstract

In this paper, we determine the maximum size of digraphs on nn vertices in which there are no two distinct walks of length 33 with the same initial vertex and the same terminal vertex. The digraphs attaining this maximum size are also characterized. Combining this with previous results, we obtain a full solution to a problem proposed by X. Zhan in 2007.

Cite

@article{arxiv.2104.08498,
  title  = {Extremal digraphs avoiding distinct walks of length 3 with the same endpoints},
  author = {Zejun Huang and Zhenhua Lyu},
  journal= {arXiv preprint arXiv:2104.08498},
  year   = {2021}
}

Comments

11 pages,2 figures

R2 v1 2026-06-24T01:16:22.176Z