A Remark on the Second Neighborhood Problem

Salman Ghazal

Abstrak

Seymour's second neighborhood conjecture states that every simple digraph (without digons) has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. Such a vertex is said to have the second neighborhood property (SNP). We define "good" digraphs and prove a statement that implies that every feed vertex of a tournament has the SNP. In the case of digraphs missing a matching, we exhibit a feed vertex with the SNP by refining a proof due to Fidler and Yuster and using good digraphs. Moreover, in some cases we exhibit two vertices with SNP

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  • 63 kali dilihat
  • 36 kali diunduh

Jurnal

Electronic Journal of Graph Theory and Applications

The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to ... tampilkan semua