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Homogeneous colourings of graphs

Tomáš Madaras; Mária Šurimová — 2023

Mathematica Bohemica

A proper vertex $k$ -colouring of a graph $G$ is called $l$ -homogeneous if the number of colours in the neigbourhood of each vertex of $G$ equals $l$ . We explore basic properties (the existence and the number of used colours) of homogeneous colourings of graphs in general as well as of some specific graph families, in particular planar graphs.

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