Fully Decomposable Split Graphs
نویسندگان
چکیده
Wediscuss various questions around partitioning a split graph into connected parts. Our main result is a polynomial time algorithm that decides whether a given split graph is fully decomposable, that is, whether it can be partitioned into connected parts of orders α1, α2, . . . , αk for every α1, α2, . . . , αk summing up to the order of the graph. In contrast, we show that the decision problemwhether a given split graph can be partitioned into connected parts of orders α1, α2, . . . , αk for a given partition α1, α2, . . . , αk of the order of the graph, is NP-hard. © 2012 Elsevier Ltd. All rights reserved.
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