Hamiltonicity and Generalised Total Colourings of Planar Graphs

Abstract

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.

Keywords

• even planar triangulation
• total colouring
• hamilton cycle
• hereditary property