Seymour's Second Neighborhood Conjecture for Tournaments Missing a Generalized Star |
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| Authors: | Salman Ghazal |
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| Affiliation: | 1. Department of Mathematics, Faculty of Sciences I, Lebanese University, , Beirut, Lebanon;2. Institute Camille Jordan, Département de Mathématiques, Université Claude Bernard Lyon 1, , France |
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| 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. © 2011 Wiley Periodicals, Inc. J Graph Theory 71:89–94, 2012 |
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| Keywords: | first out‐neighborhood second out‐neighborhood digraph median order tournament |
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