“…The clique transversal and clique independent set problems have been widely studied in Andreae et al (1991), Andreae and Flotow (1996), Andreae (1998), Balachandran et al (1996), Bandelt and Mulder (1986), Bonomo et al (2006a), Brandstädt et al (1997), Chang et al (1993Chang et al ( , 1996Chang et al ( , 2001, Dahlhaus et al (1998), Durán et al (2002Durán et al ( , 2006Durán et al ( , 2008, Erdös et al (1992), Guruswami and Rangan (2000), Lee and Chang (2006), Shan et al (2008), Xu et al (2007). Both the clique transversal and clique independent set problems are NP-hard for cocomparability graphs, planar graphs, line graphs, total graphs (Guruswami and Rangan 2000), split graphs, undirected path graphs, and k-trees with unbounded k (Chang et al 1993(Chang et al , 1996, while they are polynomial-time solvable for balanced graphs (Bonomo et al 2006a;Dahlhaus et al 1998), comparability graphs (Balachandran et al 1996), distance-hereditary graphs (Lee and Chang 2006), Helly circular-arc graphs (Guruswami and Rangan 2000;Durán et al 2008), doubly chordal graphs (Brandstädt et al 1997), and strongly chordal graphs (Brandstädt et al 1997;Chang et al 1993Chang et al , 1996.…”