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Colouring vertices of plane graphs under restrictions given by faces

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Czap J., Jendrol' S.

Discussiones Mathematicae Graph Theory

2009

tom 29

nr 3

521-543

We consider a vertex colouring of a connected plane graph G. A colour c is used k times by a face α of G if it appears k times along the facial walk of α. We prove that every connected plane graph with minimum face degree at least 3 has a vertex colouring with four colours such that every face uses some colour an odd number of times. We conjecture that such a colouring can be done using three colours. We prove that this conjecture is true for 2-connected cubic plane graphs. Next we consider other three kinds of colourings that require stronger restrictions.

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1 Discussiones Mathematicae Graph Theory

1 Czap J.

1 Jendrol' S.

1 2009

Wyniki wyszukiwania

Colouring vertices of plane graphs under restrictions given by faces