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arXiv · 1704.01389

Seymour's second neighbourhood conjecture for quasi-transitive oriented graphs

Gregory Gutin·Ruijuan Li
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Abstract

Seymour's second neighbourhood conjecture asserts that every oriented graph has a vertex whose second out-neighbourhood is at least as large as its out-neighbourhood. In this paper, we prove that the conjecture holds for quasi-transitive oriented graphs, which is a superclass of tournaments and transitive acyclic digraphs. A digraph $D$ is called quasi-transitive is for every pair $xy,yz$ of arcs between distinct vertices $x,y,z$, $xz$ or $zx$ ("or" is inclusive here) is in $D$.

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Gregory Gutin, Ruijuan Li. 2017-04-05. Seymour's second neighbourhood conjecture for quasi-transitive oriented graphs. https://arxiv.org/abs/1704.01389

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