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• W952103624 abstract "Kutatasaink temaja elsősorban extremalis grafelmelet, Ramsey elmelet grafokra es hipergrafokra, ezek alkalmazasara peldaul szamelmeletben, illetve az ezekhez kapcsolodo modszerek, elsősorban a regularitasi lemmak elmelete es alkalmazasa, a pszeudoveletlen grafok elmelete, es a graf-limeszek elmeletenek es alkalmazasainak kiepitesere, illetve vizsgalatara/alkalmazasara iranyult. Kiemelendő a pontos tetelek bizonyitasa hipergrafok extremalis, illetve Ramsey grafproblemakra (Furedi-Simonovits-Pikhurko, Haxell at al), A graf-limeszek elmeletenek kidolgozasa/alkalmazasa, (Borgs, Chayes, Lovasz, T. Sos, Vesztergombi cikksorozat, Lovasz-T. Sos, Lovasz-Szegedy cikkek, illetve Elek-Szegedy cikkek, az utobbiak nem tartoznak palyazatunkhoz.) A szamelmeleti alkalmazasok kozott emlitjuk Győri extrem grafelmeleti es hipergrafelmeleti eredmenyeit. Tovabbi eredmenyeink kozul kiemelendő a T. Sos es Saks altal inditott Bollobas-Balogh-Sos eredmenyek a grafok az oroklődő graf-tulajdonsagokkal definialt graf-izomorfiaoszalyok szamainak es a tipikus szerkezeteiknek kapcsolatarol, illetve a Balogh-Bollobas-Simonovits eredmenyek, melyek Erdos-Frankl-Rődl tetelt messze megjavitva strukturalis leirast adnak a tipikus graf-szerkezetről. | Extremal structures OTKA closing report T-032810} Miklos Simonovits Our research was primarily concentrated on extremal graph theory, Ramsey Theory, Extremal hypergraph theory their applications, e.g., in Number Theory, and the methods connected to these areas. Large part of our research is connected to quasirandom structures, Szemeredi Regularity Lemma, their connection. Recently much of the research was extended to a wider area around the Regularity Lemma, and also to the theory of graph homomorphisms, and graph limits, strongly connected to the above areas. See the results of Borgs, Chayes, Lovasz, T. Sos, Vesztergombi of Lovasz-T. Sos, etc. We have proved several sharp hypergraph extremal and Ramsey theorems. Furedi-Simonovits-Pikhurko, Haxell at al. We also mention our applications to number theory e.g. Győri's C_6 theorem, and related hypergraph results, and some coloring results. Some number theoretical analogies led to some results of T. Sos es Saks, connected also to the results of Bollobas-Balogh-Sos-Saks on hereditary properties of unlabelled graphs. Finally, we mention the improvements of the Erdős-Frankl-Rődl results, given by Balogh-Bollobas-Simonovits, on the typical structure of L-free graphs." @default.
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• W952103624 date "2007-01-01" @default.
• W952103624 modified "2023-10-15" @default.
• W952103624 title "Extremális struktúrák = Extremal structures" @default.
• W952103624 hasPublicationYear "2007" @default.
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