## The Nordhaus-Gaddum problem for the k-defective chromatic number of a P4-free graph

dc.contributor.author | Achuthan, Nirmala | |

dc.contributor.author | Achuthan, Narasimaha | |

dc.contributor.author | Simanihuruk, M. | |

dc.date.accessioned | 2017-01-30T11:27:50Z | |

dc.date.available | 2017-01-30T11:27:50Z | |

dc.date.created | 2012-02-15T20:00:47Z | |

dc.date.issued | 2011 | |

dc.identifier.citation | Achuthan, Nirmala and Achuthan, N.R. and Simanihuruk, M. 2011. The Nordhaus-Gaddum problem for the k-defective chromatic number of a P4-free graph. The Australasian Journal of Combinatorics. 49: pp. 3-13. | |

dc.identifier.uri | http://hdl.handle.net/20.500.11937/11944 | |

dc.description.abstract |
A graph is (m, k)-colourable if its vertices can be coloured with m colours such that the maximum degree of the subgraph induced on vertices receiving the same colour is at most k. The k-defective chromatic number Xk(G) of a graph G is the least positive integer m for which G is (m, k)-colourable. The Nordhaus-Gaddum problem is to find sharp bounds for Xk(G)+Xk(G) and Xk(G). Xk(G) over the set of all graphs of order p where G is the complement of the graph G. In this paper we obtain a sharp upper bound for Xk(G)+Xk(G), where G is a P4-free graph of order p and k = 1 or 2. | |

dc.publisher | Centre for Discrete Mathematics and Computing | |

dc.title | The Nordhaus-Gaddum problem for the k-defective chromatic number of a P4-free graph | |

dc.type | Journal Article | |

dcterms.source.volume | 49 | |

dcterms.source.startPage | 3 | |

dcterms.source.endPage | 13 | |

dcterms.source.issn | 1034-4942 | |

dcterms.source.title | The Australasian Journal of Combinatorics | |

curtin.department | Department of Mathematics and Statistics | |

curtin.accessStatus | Fulltext not available |