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Article Dans Une Revue The Australasian Journal of Combinatorics Année : 2021

The second neighborhood conjecture for oriented graphs missing a c4, c4,s3, chair and chair-free graph

Résumé

Seymour's Second Neighborhood Conjecture (SNC) asserts that every oriented graph has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. In this paper, we prove that if G is a graph containing no induced C4, C4¯¯¯¯¯¯, S3, chair and chair¯¯¯¯¯¯¯¯¯¯¯¯, then every oriented graph missing G satisfies this conjecture. As a consequence, we deduce that the conjecture holds for every oriented graph missing a threshold graph, a generalized comb or a star.
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Dates et versions

hal-04136272 , version 1 (15-07-2024)

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Darine Al-Mniny, Salman Ghazal. The second neighborhood conjecture for oriented graphs missing a c4, c4,s3, chair and chair-free graph. The Australasian Journal of Combinatorics, 2021, 81, pp.58-88. ⟨10.48550/arXiv.2010.10790⟩. ⟨hal-04136272⟩
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