Contributions to Seymour's Second Neighborhood Conjecture

Details Contributions to Seymour's Second Neighborhood Conjecture Contributions to Seymour's Second Neighborhood Conjecture

2008-08-07

arxiv.org/abs/0808.0946v3

Mathematics

Combinatorics

9 pages, 4 figures

Scientific paper

Let D be a simple digraph without loops or digons. For any v in V(D) let N_1(v) be the set of all nodes at out-distance 1 from v and let N_2(v) be the set of all nodes at out-distance 2. We provide sufficient conditions under which there must exist some v in V(D) such that |N_1(v)| is less than or equal to |N_2(v)|, as well as examine properties of a minimal graph which does not have such a node. We show that if one such graph exists, then there exist infinitely many strongly-connected graphs having no such vertex.

Affiliated with

Also associated with

No associations

Rating

Contributions to Seymour's Second Neighborhood Conjecture does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Contributions to Seymour's Second Neighborhood Conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Contributions to Seymour's Second Neighborhood Conjecture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-213113