@article{Bonizzoni2001NestingOP,
title={Nesting of prime substructures in k-ary relations},
author={Paola Bonizzoni and Ross M. McConnell},
journal={Theor. Comput. Sci.},
year={2001},
volume={259},
pages={341-357}
}

The modular decomposition of a graph or relation has a large number of com-binatorial applications. It divides the structure into a set of \prime" induced sub-structures, which cannot be further decomposed. Recent work on graphs and k-ary relations has focused on the discovery that prime induced substructures are densely nested when they occur. Lower bounds on the \nesting density" of prime substruc-tures in graphs are used heavily in the only known linear-time algorithm for directed graphs. We… CONTINUE READING