2024/12/28 by Hao Huang, Fei Peng, Huang, Hao +1
Engineering · Computer Science · #graph theory and CDMA systems #Digital Image Processing Techniques #Advanced Graph Theory Research
paper · pdf · doi:10.48550/arxiv.2412.20234
Seymour's celebrated second neighborhood conjecture, now more than thirty years old, states that in every oriented digraph, there is a vertex u such that the size of its second out-neighborhood N++(u) is at least as large as that of its first out-neighborhood N+(u). In this paper, we prove the existence of u for which |N++(u)| ≥ 0.715538 |N+(u)|. This result provides the first improvement to the best known constant factor in over two decades.