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КартаВръзкиТемиБългарияНощта (K-TRIO)Мария Склодовска-КюриЗа ученициЗа учителиМетодологияИзненадай ме
HEИндивидуална стипендия2025–2027

PARTIORI · Rainbow partitions and oriented structures in random graphs

„Хоризонт Европа“ — Действия „Мария Склодовска-Кюри“

Период
2025-09-15 → 2027-09-14
Финансиране от ЕС
209 915 €
Участници
2
Схема
HORIZON-TMA-MSCA-PF-EF

Линиите свързват координатора с партньорите.

Накратко на български

Математическите структури в случайни графи се изследват чрез разлагане на цветни пътища и търсене на ориентирани обекти. Тези методи помагат за подобряване на биологичните експерименти, откриването на грешки в мрежи и създаването на по-сигурни кодове за предаване на данни.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Цел на проекта

Combinatorial designs are some of the most fascinating and elusive objects in mathematics. For over 200 years their study has generated many sophisticated methods, and the theory has found applications in biological experiment design, construction of strong error correcting codes, and network fault detection. The celebrated proof of the existence of designs has been an impressive achievement of the last decade. At the core of this landmark result lies a combination of powerful contemporary tools: the semi-random and absorption methods. The PARTIORI project seeks to utilise and extend these ideas to demonstrate the existence of certain transversal partitions and large oriented structures of, respectively, coloured an oriented random graphs.At the intersection of combinatorial design theory, Ramsey theory, and probabilistic combinatorics, PARTIORI lies at the edge of active sub-areas, exploring rainbow decompositions of edge-coloured random graphs and thresholds for the emergence of an Ramsey property of graph orientations. More precisely, the project aims at leveraging powerful methods from extremal and probabilistic combinatorics (the semi-random, absorption, regularity and container methods) to make significant contributions to the following two areas:- obtaining decompositions of edge-coloured complete graphs into few rainbow paths;- establishing universality results for the containment of oriented structures in arbitrary orientations of random graphs.The research is planned for two years and takes as a basis prior results obtained by the applicant while also taking advantage of approaches developed by the host. A secondment at the University of Warwick (U.K.) is also planned, hosted by Prof. Richard Montgomery, a leading figure in mathematics and expert in both topics covered by the project.

Оригинален текст от CORDIS (на английски).

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Данни: CORDIS, © Европейски съюз