Colouring vertices of plane graphs under restrictions given by faces
Július Czap, Stanislav Jendrol' (2009)
Discussiones Mathematicae Graph Theory
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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...