Kombinatorikus módszerek a diszkrét geometriában = Combinatorial methods in discrete geometry

Bárány, Imre and Füredi, Zoltán and Kincses, János and Pach, János and Pór, Attila and Solymosi, Jozsef and Tóth, Géza (2011) Kombinatorikus módszerek a diszkrét geometriában = Combinatorial methods in discrete geometry. Project Report. OTKA.

Preview

Text 60427_ZJ1.pdf Download (105kB) | Preview

Abstract

Barany Imre veletlen politopokkal, a Tverberg tetel altalanositasaival, a topologia es kombinatorikus geometria hatarteruletevel foglalkozott. Ugyanezen a teruleten dolgozott Kincses Janos, es meg politopok kombinatorikajan. Furedi Zoltan a ter illetve egy korlatos halmaz gazdasagos fedeseivel, grafok pakolasaival foglalkozott. Solymosi Jozsef additiv kombinatorikaval illetve additiv szamelmelettel foglalkozott, elsosorban azzal, hogy egy n elemu A szamhalmaz eseten legalabb mekkora az |A+A|+|A*A| ertek. Ezenkivul a Szemeredi-Trotter illetve Pach-Sharir tetelhez hasonlo incidencia tetelt bizonyotott magas dimenzios algebrai gorbekre. Ez utobbi eredmeny nagyon igeretes kezdetnek tunik. Toth Geza grafok metszesi szamaval es lerajzolasaival foglalkozott, konstualt egy grafot, amelynek a par-metszesi szama es paratlen-metszesi szama elter. Pach Janossal tanulmanyoztak grafok sikbeli es magasabb genuszu feluleten vett metszesi szamait, illetve az ezek kozti osszefuggeseket. A sik illetve a ter sokszoros fedeseinek szetbonthatosagat is vizsgalta. Pach Janossal azt vizsgaltak, hogy konvex halmazok rendtipusa mikor reprezentalhato pontokkal. Pach Janos Jacob Fox-szal a Lipton-Tarjan szeparator tetelt altalanositotta sikgrafokrol kulonbozo mas tipusu grafokra, peldaul konvex halmazok illetve gorbek metszetgrafjara. Por Attila lathatosagi grafokkal illetve grafok Kneser-reprezentaciojaval foglalkozott, amely szoros kapcsolatban van a frakcionalis kromatikus szammal. | Imre Barany investigated random polytopes, generalizations of the Tverberg theorem, and problems on the boundary of combinatorial geometry and topology. Janos Kincses also worked in this latter area, and also studied combinatorics of polytopes. Zoltan Furedi studied economical coverings of the space, or a bounded set. He also obtained important results concerning packings of small graphs into a large graph. Jozsef Solymosi worked in additive combinatorics and additive number theory. He investigated especially the question that at least how large is |A+A|+|A*A| if A is a set of n numbers. He also proved an incidence result for high dimensional algebraic curves, similar to the Szemeredi-Trotter or the Pach-Sharir theorems. This result seems to be a good start. Geza Toth investigated crossing numbers and drawings of graphs. He constructed a graph whose pair-crossing number is larger than its odd-crossing number. With Janos Pach he studied relationships between crossing numbers of graphs on different surfaces. He also obtained results on the decomposability of multiple coverings of the plane or space. With Janos Pach he studied, under what conditions can the order type of convex sets be represented by points. Janos Pach, together with Jacob Fox, generalized the Lipton-Tarjan separator theorem for planar graphs, for intersection graphs of convex sets, and for intersection graphs of curves. Attila Por obtained results on visibility graphs and on Kneser representations of graphs.

Actions (login required)

Edit Item