Abstract
Let be a simple digraph without loops or digons. For any let be the set of all nodes at out-distance 1 from and let be the set of all nodes at out-distance 2. We show that if the underlying graph is triangle-free, there must exist some such that . We provide several properties a “minimal” graph which does not contain such a node must have. Moreover, we show that if one such graph exists, then there exist infinitely many.
Citation
James Brantner. Greg Brockman. Bill Kay. Emma Snively. "Contributions to Seymour's second neighborhood conjecture." Involve 2 (4) 387 - 395, 2009. https://doi.org/10.2140/involve.2009.2.387
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