We discuss 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, i.e., whether it can be partitioned into connected parts of order a 1,a 2,...,a k for every a 1,a 2,...,a k summing up to the order of the graph. In contrast, we show that the decision problem whether a given split graph can be partitioned into connected parts of order a 1,a 2,...,a k for a given partition a 1,a 2,...,a k of the order of the graph, is NP-hard.
|Title of host publication||Combinatorial Algorithms (20th International Workshop, IWOCA 2009, Hradec nad Moravici, Czech Republic, June 28-July 2, 2009, Revised Selected Papers)|
|Editors||J. Fiala, J. Kratochvil, M. Miller|
|Place of Publication||Berlin|
|Publication status||Published - 2009|
|Name||Lecture Notes in Computer Science|