On Seymour's Second Neighborhood Conjecture of m-free Digraphs

Hao Liang; Jun-Ming Xu

On Seymour's Second Neighborhood Conjecture of m-free Digraphs

Combinatorics 2017-01-03 v1

Authors: Hao Liang , Jun-Ming Xu

Abstract

This paper gives an approximate result related to Seymour's Second Neighborhood conjecture, that is, for any $m$ -free digraph $G$ , there exists a vertex $v\in V(G)$ and a real number $\lambda_m$ such that $d^{++}(v)\geq \lambda_m d^+(v)$ , and $\lambda_m \rightarrow 1$ while $m \rightarrow +\infty$ . This result generalizes and improves some known results in a sense.

Keywords

Seymour's second neighborhood conjecture m-free digraphs directed graphs second neighborhood approximation result

Cite

@article{arxiv.1701.00328,
  title  = {On Seymour's Second Neighborhood Conjecture of m-free Digraphs},
  author = {Hao Liang and Jun-Ming Xu},
  journal= {arXiv preprint arXiv:1701.00328},
  year   = {2017}
}

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