Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
The total generalised colourings considered in this paper are colourings of graphs such that the vertices and edges of the graph which receive the same colour induce subgraphs from two prescribed hereditary graph properties while incident elements receive different colours. The associated total chromatic number is the least number of colours with which this is possible. We study such colourings for sets of planar graphs and determine, in particular, upper bounds for these chromatic numbers for proper colourings of the vertices while the monochromatic edge sets are allowed to be forests. We also prove that if an even planar triangulation has a Hamilton cycle H for which there is no cycle among the edges inside H, then such a graph needs at most four colours for a total colouring as described above. The paper is concluded with some conjectures and open problems.
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
243-257
Opis fizyczny
Daty
wydano
2016-05-01
otrzymano
2014-06-18
poprawiono
2015-12-07
zaakceptowano
2016-02-12
online
2016-04-15
Twórcy
autor
- Faculty of Mathematics, Computer Science and Econometrics University of Zielona Góra, M.Borowiecki@wmie.uz.zgora.pl
autor
- Department of Mathematics and Applied Mathematics University of Pretoria, izak.broere@up.ac.za
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1874