Total colouring of plane graphs with maximum degree nine
Résumé
The central problem of the total-colorings is the total-coloring conjecture, which asserts that every graph of maximum degree D admits a (D+2)-total-coloring. Similar to edge-colorings—with Vizing's edge-coloring conjecture—this bound can be decreased by 1 for plane graphs of higher maximum degree. More precisely, it is known that if D > 9, then every plane graph of maximum degree D is (D+1)-totally-colorable. On the other hand, such a statement does not hold if D < 4. We prove that every plane graph of maximum degree 9 can be 10-totally-colored.
Domaines
Mathématique discrète [cs.DM]
Origine : Fichiers produits par l'(les) auteur(s)
Loading...