Hamiltonicity and Generalised Total Colourings of Planar Graphs

Mieczysław Borowiecki, and Izak Broere. "Hamiltonicity and Generalised Total Colourings of Planar Graphs." Discussiones Mathematicae Graph Theory 36.2 (2016): 243-257. <http://eudml.org/doc/277131>.

@article{MieczysławBorowiecki2016,
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. 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.},
author = {Mieczysław Borowiecki, Izak Broere},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {even planar triangulation; total colouring; Hamilton cycle; hereditary property},
language = {eng},
number = {2},
pages = {243-257},
title = {Hamiltonicity and Generalised Total Colourings of Planar Graphs},
url = {http://eudml.org/doc/277131},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Mieczysław Borowiecki
AU - Izak Broere
TI - Hamiltonicity and Generalised Total Colourings of Planar Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 2
SP - 243
EP - 257
AB - 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.
LA - eng
KW - even planar triangulation; total colouring; Hamilton cycle; hereditary property
UR - http://eudml.org/doc/277131
ER -