On minimum t-claw deletion in split graphs
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For t≥ 3, K_1, t is called t-claw. In minimum t-claw deletion problem (), given a graph G=(V, E), it is required to find a vertex set S of minimum size such that G[V∖ S] 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 (). Given a bipartite graph G=(A ∪ B, E), in it is asked to find a vertex set S of minimum size such that G[V ∖ S] has no t-claw with the center vertex in A. A primal-dual algorithm approximates within a factor of t. We prove that it is -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 , we prove that is -hard to approximate within a factor better than t, for split graphs. We also consider their complementary maximization problems and prove that they are -complete.
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