4 research outputs found
Extremális és véletlen struktúrák = Extremal and random structures
RĂ©sztvevĹ‘k: T. SĂłs Vera, akadĂ©mikus, SzemerĂ©di Endre, akadĂ©mikus, FĂĽredi Zoltán akadĂ©mikus, GyĹ‘ri Ervin, a tudományok doktora, Elek Gábor a tudományok doktora, Ă©s tĂ©mavezetĹ‘kĂ©nt Simonovits MiklĂłs (akadĂ©mikus). Menetközben csatlakozott a pályázathoz PatkĂłs Balázs. Itt, a rövid beszámolĂłban csak a legfontosabb tĂ©mákat emlĂtem, Klasszikus Extremális Ă©s Ramsey problĂ©mák megoldása, ill. ezekkel rokon problĂ©mák. A SzemerĂ©di Regularitási Lemma alkalmazásai, az extremális Ă©s Ramsey tĂpusĂş kĂ©rdĂ©sek kapcsolata, ezek kapcsolata a kvázivĂ©letlensĂ©ggel, ""tulajdonság-tesztelĂ©ssel"". Az extrĂ©m gráfelmĂ©lettel szoros kapcsolatban állĂł ErdĹ‘s-Kleitman-Rothschild tĂpusĂş tĂ©telek. A gráflimesz vizsgálata, alkalmazásai HasonlĂłságok Ă©s kĂĽlönbsĂ©gek a sűrű Ă©s ritka gráfok limesz-elmĂ©letĂ©ben. ,,Sporadikus kĂ©rdĂ©sek,'' pl. algebrai Ă©s geometriai alkalmazások. | Project leader: MiklĂłs Simonovits Participants: Vera T. SĂłs , Endre SzemerĂ©di, Zoltán FĂĽredi, Ervin GyĹ‘ri, Gábor Elek. Balázs PatkĂłs joined our group later. Here I have space only to mention the topics breafly. We were interested primarily in the connection, similarities and differences between deterministic and randomlike structures. Large part of our research was related to the SzemerĂ©di Regularity Lemma and its various versions, and the applications of it, among others, in classical extremal graph and hypergraph problems. We also investigated the application of this lemma in quasi-randomness, property testing, and other related fields. We investigated the graph-limit theory, both for dense and veryy sparse graph sequences. Beside these, we investigated several ``Sporadic question,'' e.g. applications of our methods in algebra and geometry
An improved bound for the monochromatic cycle partition number
AbstractImproving a result of Erdős, Gyárfás and Pyber for large n we show that for every integer r⩾2 there exists a constant n0=n0(r) such that if n⩾n0 and the edges of the complete graph Kn are colored with r colors then the vertex set of Kn can be partitioned into at most 100rlogr vertex disjoint monochromatic cycles
Quadripartite version of the Hajnal–Szemerédi Theorem
Let G be a quadripartite graph with N vertices in each vertex class and each vertex is adjacent to at least (3/4)N vertices in each of the other classes. There exists an N0 such that, if N ≥ N0, then G contains a subgraph that consists of N vertex-disjoint copies of K4