3 research outputs found
Kombinatorikus Optimalizálás: Algoritmusok, Strukturák, Alkalmazások = Combinatorial optimization: algorithms, structures, applications
Mint azt az OTKA-pályázat munkaterve tartalmazza, a pályázatban rĂ©sztvevĹ‘ kutatĂłk alkotják a tĂ©mavezetĹ‘ irányĂtásával működĹ‘ Egerváry JenĹ‘ Kombinatorikus Optimalizálási KutatĂłcsoportot. A csoport a kutatási tervben szereplĹ‘ több tĂ©mában jelentĹ‘s eredmĂ©nyeket Ă©rt el az elmĂşlt 4 Ă©vben, ezekrĹ‘l a pályázat rĂ©sztvevĹ‘inek több mint 50 folyĂłiratcikke jelent meg, Ă©s számos rangos nemzetközi konferencián ismertetĂ©sre kerĂĽltek. NĂ©hány kiemelendĹ‘ eredmĂ©ny: sikerĂĽlt polinomiális kombinatorikus algoritmust adni irányĂtott gráf pont-összefĂĽggĹ‘sĂ©gĂ©nek növelĂ©sĂ©re; jelentĹ‘s elĹ‘relĂ©pĂ©s törtĂ©nt a háromdimenziĂłs tĂ©rben merev gráfok jellemzĂ©sĂ©vel Ă©s a molekuláris sejtĂ©ssel kapcsolatban; 2 dimenziĂłban sikerĂĽlt bizonyĂtani Hendrickson sejtĂ©sĂ©t; a párosĂtáselmĂ©letben egy Ăşjdonságnak számĂtĂł mĂłdszerrel számos Ăşj algoritmikus eredmĂ©ny szĂĽletett; több, gráfok Ă©lösszefĂĽggĹ‘sĂ©gĂ©t jellemzĹ‘ tĂ©telt sikerĂĽlt hipergráfokra általánosĂtani. | As the research plan indicates, the researchers participating in the project are the members of the Egerváry Research Group, led by the coordinator. The group has made important progress in the past 4 years in the research topics declared in the research plan. The results have been published in more than 50 journal papers, and have been presented at several prestigious international conferences. The most significant results are the following: a polynomial algorithm has been found for the node-connectivity augmentation problem of directed graphs; considerable progress has been made towards the characterization of 3-dimensional rigid graphs and towards the proof of the molecular conjecture; Hendrickson's conjecture has been proved in 2 dimensions; several new algorithmic results were obtained in matching theory using a novel approach; several theorems characterizing connectivity properties of graphs have been generalized to hypergraphs