New strong colouring of hypergraphs

• Published in: Le Matematiche
• Main Authors: Sandro Rajola, Maria Scafati Tallini
• Format: Article
• Language: English
• Published: Università degli Studi di Catania 2011-06-01
• Subjects: Graph; Hypergraph; Colouring.
• Online Access: http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/854

We define a new colouring for a hypergraph, in particular for a graph. Such a method is a partition of the vertex-set of a hypergraph, in particular of a graph. However, it is more intrinsically linked to the geometric structure of the hypergraph and therefore enables us to obtain stronger results than in the classical case. For instance, we prove theorems concerning 3-colourings, 4-colourings and 5-colourings, while we have no analogous results in the classical case. Moreover, we prove that there are no semi-hamiltonian regular simple graphs admitting a hamiltonian 1-colouring. Finally, we characterize the above graphs admitting a hamiltonian 2-colouring and a hamiltonian 3-colouring.<br />