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- W2134301227 abstract "The question of whether a graph can be partitioned into k independent dominating sets, which is the same as having a fall k - colouring , is considered. For k = 3 , it is shown that a graph G can be partitioned into three independent dominating sets if and only if the cartesian product G □ K 2 can be partitioned into three independent dominating sets. The graph K 2 can be replaced by any graph H such that there is a mapping f : Q n → H , where f is a type-II graph homomorphism. The cartesian product of two trees is considered, as well as the complexity of partitioning a bipartite graph into three independent dominating sets, which is shown to be NP-complete. For other values of k , iterated cartesian products are considered, leading to a result that shows for what values of k the hypercubes can be partitioned into k independent dominating sets." @default.
- W2134301227 created "2016-06-24" @default.
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- W2134301227 date "2009-01-01" @default.
- W2134301227 modified "2023-10-02" @default.
- W2134301227 title "Fall colouring of bipartite graphs and cartesian products of graphs" @default.
- W2134301227 cites W2000838329 @default.
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- W2134301227 doi "https://doi.org/10.1016/j.dam.2008.03.003" @default.
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