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arxiv: 2001.07242 · v1 · pith:FQL3ABDPnew · submitted 2020-01-20 · 🧮 math.CO

A generalisation of Seymour's second neighbourhood conjecture

Jeck Lim This is my paper
classification 🧮 math.CO
keywords conjecturegeneralisationneighbourhoodsecondseymourcasedirectedgraphs
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In this note we propose a generalisation of Seymour's Second Neighbourhood Conjecture to two directed graphs on a vertex set. We prove that this generalisation holds in the case of tournaments, and we show that a natural strengthening of this conjecture does not hold.

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  1. A proof of Seymour's second neighborhood conjecture for oriented graphs with minimum out-degree equal to 7

    math.CO 2026-06 unverdicted novelty 6.0

    Authors prove Seymour's second neighborhood conjecture for oriented graphs with minimum out-degree 7 via local reductions followed by computer-assisted infeasibility checks on finite obstructions.