Constrained Hitting Set and Steiner Tree in SCk and 2K2-free Graphs

Strictly Chordality-k graphs (SC k ) are graphs which are either cycle-free or every induced cycle is of length exactly k, k ≥ 3. Strictly chordality-3 and strictly chordality-4 graphs are well known chordal and chordal bipartite graphs, respectively.For k ≥ 5, the study has been recently initiated in [1] and various structural and algorithmic results are reported.In this paper, we study SC k graphs in the algorithmic front and the study concerns the class of graphs where k ≥ 5. We show that recognizing vertex cycle ordering (VCO) for SC k , k ≥ 5 graphs, maximum independent set (MIS), minimum vertex cover, minimum dominating set, feedback vertex set (FVS), odd cycle transversal (OCT), even cycle transversal (ECT) and Steiner tree problem are linear time solvable on SC k graphs, k ≥ 5. We next consider 2K 2 -free graphs and discussed the algorithmic problems such as FVS, OCT, ECT and Steiner tree problem on the subclasses of 2K 2 -free graphs.