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| HAL : hal-00686989, version 2 |
| arXiv : 1204.2519 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (11-04-2012) | v2 (03-01-2013) |
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| A new bound for the 2/3 conjecture |
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| Daniel Král' 1Chun-Hung Liu 2 |
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| LEA STRUCO Collaboration(s) |
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| (03/2012) |
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| We show that any n-vertex complete graph with edges colored with three colors contains a set of at most four vertices such that the number of the neighbors of these vertices in one of the colors is at least 2n/3. The previous best value, proved by Erdos, Faudree, Gould, Gyárfás, Rousseau and Schelp in 1989, is 22. It is conjectured that three vertices suffice. |
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| 1 : | Centre for Discrete Mathematics and its Applications [Warwick] (DIMAP) |
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University of Warwick |
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| 2 : | School of Mathematics - Georgia Institute of Technology |
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Georgia Institute of Technology (Georgia Tech) |
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| 3 : | ORPAILLEUR (INRIA Nancy - Grand Est / LORIA) |
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INRIA – CNRS : UMR7503 – Université de Lorraine |
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| 4 : | Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA) |
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CNRS : UMR7089 – Université Paris VII - Paris Diderot |
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| Domaine | : | Informatique/Mathématique discrète Mathématiques/Combinatoire |
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| Monochromatic domination – colored complete graph – flag algebra |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00686989, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00686989 | |
| oai:hal.archives-ouvertes.fr:hal-00686989 | |
| Contributeur : Jean-Sébastien Sereni | |
| Soumis le : Jeudi 3 Janvier 2013, 11:03:58 | |
| Dernière modification le : Mardi 8 Janvier 2013, 15:49:50 | |
