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CHROMPART

Partition calculus on graphs, digraphs and hypergraphs with uncountable chromatic number

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EC-Contrib. €

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 CHROMPART project word cloud

Explore the words cloud of the CHROMPART project. It provides you a very rough idea of what is the project "CHROMPART" about.

hypergraphs    ramsey    preservation    finite    theme    deeper    shelah    themes    dimensional    underlie    significantly    guide    satisfy    scheme    calculus    crucially    chromatic    combinatorics    meeting    raised    logic    arguments    oscillation    structural    relations    point    varying    hindman    works    infinite    diestel    motivate    todorcevic    dichromatic    negative    komj    theorems    ramification    investigations    solving    hajnal    forcing    hence    partition    dimensions    our    erd    complete    tools    questions    walks    mixed    global    places    finitary    emphasis    minimal    maps    purely    digraphs    thomassen    graph    existence    fact    combinatorial    iteration    explore    foundational    theory    first    infinitary    aacute    necessarily    techniques    orientations    interactions    central    graphs    obligatory    1960s    deep    complement    lastly    relate    local    uncountable    hypergraph    construction    zfc   

Project "CHROMPART" data sheet

The following table provides information about the project.

Coordinator	UNIVERSITY OF EAST ANGLIA    more Organization address address: EARLHAM ROAD city: NORWICH postcode: NR4 7TJ website: http://www.uea.ac.uk contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.
Coordinator Country	United Kingdom [UK]
Total cost	224˙933 €
EC max contribution	224˙933 € (100%)
Programme	1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
Code Call	H2020-MSCA-IF-2018
Funding Scheme	MSCA-IF-EF-ST
Starting year	2020
Duration (year-month-day)	from 2020-03-01   to  2022-02-28

 Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	UNIVERSITY OF EAST ANGLIA × UNIVERSITY OF EAST ANGLIA Organization address address: EARLHAM ROAD city: NORWICH postcode: NR4 7TJ website: http://www.uea.ac.uk contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a. Close	UK (NORWICH)	coordinator	224˙933.00

Map

 Project objective

Our main goal is to develop the theory of partition calculus on graphs, digraphs and hypergraphs with emphasis on interactions between one-and multi-dimensional relations. Such global characteristics crucially depend on local, often finitary structural properties. This places our project at the meeting point of finite and infinite combinatorics with logic and set theory. Some of the most important questions that motivate our investigations were first raised by P. ErdÅ‘s and A. Hajnal in the 1960s. Their problems still guide research across finite and infinite combinatorics including the most recent works of R. Diestel, N. Hindman, P. Komjáth, C. Thomassen, S. Todorcevic, and S. Shelah. Our main objective is to investigate ramification arguments between Ramsey-results of varying dimensions. In fact, (1) we study if graphs with uncountable chromatic number necessarily satisfy the same higher-dimensional negative partition relations as uncountable complete graphs. We relate this theme to (2) the existence of orientations with large dichromatic number and partition relations on digraphs. Lastly, we explore a novel concept, (3) the existence of oscillation maps on the obligatory hypergraph associated to a graph with uncountable chromatic number. Our program will be carried out through solving specific, often well-known open problems that are central to these themes. We aim to study both the purely combinatorial and the deep foundational issues that underlie these questions. Hence, we will complement the use of advanced forcing techniques from set theory (such as mixed side-condition methods and new iteration preservation theorems) with novel combinatorial tools, such as minimal walks, oscillation maps and various ZFC construction scheme techniques. We expect our research to produce new methods of wide impact and a significantly deeper understanding of the interactions of finite and infinitary combinatorics.

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