On characterization and recognition of proper tagged probe interval graphs

Interval graphs were used in the study of the human genome project by the molecular biologist Benzer. Later on probe interval graphs were introduced by Zhang as a generalization of interval graphs for the study of cosmid contig mapping of DNA. Further research in this area required more useful and cost-effective tools. The concept of tagged probe interval graphs is motivated from this point of view. In this paper, we consider a natural subclass of it, namely, the class of proper tagged probe interval graphs. In this paper, we present a characterization theorem and a linear time recognition algorithm for proper tagged probe interval graphs. Also, we discuss the interrelations between the classes of proper tagged probe interval graphs and tagged probe interval graphs with probe interval graphs and probe proper interval graphs.