Obtaining Split Graphs by Edge Contraction.

We study the parameterized complexity of the following Split Contraction problem: Given a graph G, and an integer k as parameter, determine whether G can be modified into a split graph by contracting at most k edges. We show that Split Contraction can be solved in FPT time 2 O ( k 2 ) n 5 , but admits no polynomial kernel unless NP ¿ coNP / poly .