The NordhausGaddum problem for the kdefective chromatic number of a P4free graph
Citation
Achuthan, Nirmala and Achuthan, N.R. and Simanihuruk, M. 2011. The NordhausGaddum problem for the kdefective chromatic number of a P4free graph. The Australasian Journal of Combinatorics. 49: pp. 313.
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The Australasian Journal of Combinatorics
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Department of Mathematics and Statistics
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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 kdefective chromatic number Xk(G) of a graph G is the least positive integer m for which G is (m, k)colourable. The NordhausGaddum 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 P4free graph of order p and k = 1 or 2.
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