New strong colouring of hypergraphs
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 t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Università degli Studi di Catania
2011-06-01
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| Series: | Le Matematiche |
| Subjects: | |
| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/854 |
| Summary: | 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 /> |
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| ISSN: | 0373-3505 2037-5298 |