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Graph colouring and its application within cartography (CROSBI ID 638552)

Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija

Glaurdić, Mate ; Beban-Brkić, Jelka Graph colouring and its application within cartography // Book of abstracts of the 19th Scientific- Professional Colloquium on Geometry and Graphics, Starigrad Paklenica, September 4-8, 2016 / Došlić, Tomislav ; Jurkin, Ema (ur.). Zagreb: Hrvatsko društvo za geometriju i grafiku, 2016. str. 23-23

Podaci o odgovornosti

Glaurdić, Mate ; Beban-Brkić, Jelka

engleski

Graph colouring and its application within cartography

The problem of colouring geographical political maps has historically been associated with the theory of graph colouring. In the middle of the 19th century the following question was posed: how many colours are needed to colour a map in a way that countries sharing a border are coloured differently. The solution has been reached by linking maps and graphs. It took more than a century to prove that 4 colours are sufficient to create a map in which neighbouring countries have different colours. In graph theory, graph colouring is a special case of graph labelling. It is about assigning a colour to graph elements: vertices, edges, regions, with certain restrictions. With this presentation we would like to assess the elements of the theory of graph colouring with an emphasis on its application on practical problems in the field of surveying namely cartography. A mathematical basis for administrative map colouring will be given along with the chronology of proving The 4 Colour Theorem. In addition, World maps and map of Croatia will be shown, to determine the minimum number of colours needed to colour a map properly in practice. Application Cartography is a discipline that deals with collecting, processing, storing and usage of spatial information, being especially concerned in their visualisation i.e. cartographic representation. A map is a connected planar graph where all vertices have a degree of at least 3. It is a unit consisting of interconnected regions/countries. The border of each region represents a closed curve that can be divided into as many parts/edges as the region has neighbours. The two countries that share a common edge are considered adjacent. As well as being a tool that is used for better orientation in space and for travel from point A to point B, maps also possess an artistic component. Each colour causes a certain stimulus therefore it is necessary to pay special attention to the choice of colours and their diversity when producing a map. Selecting the optimal number of colours is also valuable because it enables cheaper reproduction of maps.

graph ; graph colouring ; map ; map colouring ; 4 colour theorem

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

Podaci o prilogu

23-23.

2016.

objavljeno

Podaci o matičnoj publikaciji

Book of abstracts of the 19th Scientific- Professional Colloquium on Geometry and Graphics, Starigrad Paklenica, September 4-8, 2016

Došlić, Tomislav ; Jurkin, Ema

Zagreb: Hrvatsko društvo za geometriju i grafiku

Podaci o skupu

19th Scientific-Professional Colloquium on Geometry and Graphics

predavanje

05.09.2016-08.09.2016

Starigrad, Hrvatska

Povezanost rada

Matematika, Geodezija