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

2017/01/02 by Hao Liang, Liang, Hao, Jun‐Ming Xu +1
Computer Science · Mathematics · #05C20 #05C38 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1701.00328

openalex publication_date 2017/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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∈ V(G) and a real number λ_m such that d⁺⁺(v)≥ λ_m d⁺(v), and λ_m → 1 while m → +∞. This result generalizes and improves some known results in a sense.

Related

• An improved bound on Seymour's second neighborhood conjecture
• Seymour's Second Neighborhood Conjecture for Subsets of Vertices
• Seymour's second-neighborhood conjecture from a different perspective
• Contributions to Seymour's Second Neighborhood Conjecture
• A note on the second neighborhood problem for k-anti-transitive and m-free digraphs