Application of the Four Colour Theorem to Identify Spatial Regional Poles and Turnpikes of Economic Growth

A. Jakimowicza, D. Rzeczkowskib aInstitute of Economics, Polish Academy of Sciences, Palace of Culture and Science, Pl. Defilad 1, PL-00901 Warsaw, Poland bDepartment of Quantitative Methods, Faculty of Economic Sciences, University of Warmia and Mazury in Olsztyn, M. Oczapowskiego 4, PL-10719 Olsztyn, Poland

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This paper presents a method for identifying regional poles and the turnpikes of growth based on the following foundations: four colour theorem, Wikinomics business model in the form of platforms for participation, evaluation of the functionality of websites run by public administration municipal offices, and dual graph reduction. The province of Warmia and Mazury, which is the subject of the study, is one of the poorest provinces in Poland in terms of economic development. It is therefore natural that the growth of this region requires external enterprise sources. This role can be best performed primarily by websites run by municipal offices, which initiate business activity in their corresponding areas, and consequently, can be regarded as Wikinomics platforms of participation. Using the k-means clustering method, these websites were divided into four separate quality classes. These classes were assigned four various colours, which were subsequently used for preparing the map of the province. Each municipality was marked with a colour corresponding to the quality class of the website run by the state administration unit operating in a given area. The system of colours resulting from the four colour theorem and a corresponding dual graph serve as a frame of reference with regard to each empirical colour distribution and to another, related, dual graph. Thus, the four colour theorem describes the largest diversity of regional growth poles. The measure of the economic growth of the region is a degree of reduction of the dual graph corresponding to the empirical colour distribution, which identifies actual growth poles and determines the turnpikes of growth. The ultimate development objective, although not always achievable, is a reduction of the dual graph to a single vertex, when all municipal offices in the province have websites of the highest quality.

DOI:10.12693/APhysPolA.133.1362 PACS numbers: 89.65.Gh, 02.10.Ox