Show simple item record

dc.contributor.authorAchuthan, Nirmala
dc.contributor.authorAchuthan, Narasimaha
dc.contributor.authorSimanihuruk, M.
dc.identifier.citationAchuthan, 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.

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.publisherCentre for Discrete Mathematics and Computing
dc.titleThe Nordhaus-Gaddum problem for the k-defective chromatic number of a P4-free graph
dc.typeJournal Article
dcterms.source.titleThe Australasian Journal of Combinatorics
curtin.departmentDepartment of Mathematics and Statistics
curtin.accessStatusFulltext not available

Files in this item


This item appears in the following Collection(s)

Show simple item record