Seymour's second neighborhood conjecture for tournaments missing a generalized star
arXiv:1106.0085 · doi:10.1002/jgt.20634
Abstract
Seymour's Second Neighborhood Conjecture asserts that every digraph (without digons) has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. We prove its weighted version for tournaments missing a generalized star. As a consequence the weighted version holds for tournaments missing a sun, star, or a complete graph.
arXiv commentAccepted for publication in Journal of Graph Theory in 24 June 2011