About the second neighborhood problem in tournaments missing disjoint stars
<p>Let $D$ be a digraph without digons. Seymour's second neighborhood conjecture states that $D$ has a vertex $v$ such that $d^+(v) \leq d^{++}(v)$. Under some conditions, we prove this conjecture for digraphs missing $n$ disjoint stars. Weaker conditions are required when $n = 2$ or $3$....
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| Format: | Article |
| Language: | English |
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Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
2016-10-01
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| Series: | Electronic Journal of Graph Theory and Applications |
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| Online Access: | https://www.ejgta.org/index.php/ejgta/article/view/189 |
| Summary: | <p>Let $D$ be a digraph without digons. Seymour's second neighborhood conjecture states that $D$ has a vertex $v$ such that $d^+(v) \leq d^{++}(v)$. Under some conditions, we prove this conjecture for digraphs missing $n$ disjoint stars. Weaker conditions are required when $n = 2$ or $3$. In some cases we exhibit two such vertices.</p> |
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| ISSN: | 2338-2287 |