Co-TT graphs and a characterization of split co-TT graphs

In this paper, we present a new characterization of complement Threshold Tolerance graphs (co-TT for short) and find a recognition algorithm for the subclass of split co-TT graphs running in O(n2)O(n2) time. Currently, the best recognition algorithms for co-TT graphs and for split co-TT graphs run in O(n4)O(n4) time (Hammer and Simeone (1981) [4]; Monma et al. (1988) [7]).