For tβ₯3, K1,tβ is called t-claw. In minimum t-claw deletion
problem (\texttt{Min-t-Claw-Del}), given a graph G=(V,E), it is required
to find a vertex set S of minimum size such that G[VβS] is
t-claw free. In a split graph, the vertex set is partitioned into two sets
such that one forms a clique and the other forms an independent set. Every
t-claw in a split graph has a center vertex in the clique partition. This
observation motivates us to consider the minimum one-sided bipartite t-claw
deletion problem (\texttt{Min-t-OSBCD}). Given a bipartite graph G=(AβͺB,E), in \texttt{Min-t-OSBCD} it is asked to find a vertex set S of
minimum size such that G[VβS] has no t-claw with the center
vertex in A. A primal-dual algorithm approximates \texttt{Min-t-OSBCD}
within a factor of t. We prove that it is \UGC-hard to approximate with a
factor better than t. We also prove it is approximable within a factor of 2
for dense bipartite graphs. By using these results on \texttt{Min-t-OSBCD},
we prove that \texttt{Min-t-Claw-Del} is \UGC-hard to approximate within a
factor better than t, for split graphs. We also consider their complementary
maximization problems and prove that they are \APX-complete.Comment: 11 pages and 1 figur