Directed Graphs of Entanglement Two

Entanglement is a complexity measure for directed graphs that was used to show that the variable hierarchy of the propositional modal µ-calculus is strict. While graphs of entanglement zero and one are indeed very simple, some graphs of entanglement two already contain interesting nesting of cycles. This motivates our study of the class of graphs of entanglement two, as these are both simple in a sense and already complex enough for modelling certain structured systems. Undirected graphs of entanglement two were already studied by Belkhir and Santocanale and a structural decomposition for such graphs was given. We study the general case of directed graphs of entanglement two and prove that they can be decomposed as well, in a way similar to the known decompositions for tree-width, DAG-width and Kelly-width. Moreover, we show that all graphs of entanglement two have Kelly-width at most three. It is known that such graphs also have DAG-width at most three [2]. Since there exist both gra...

• Type: Conference
• Year: 2009
• Where: FCT
• Authors: Erich Grädel, Lukasz Kaiser, Roman Rabinovich
• Keywords: Certain Structured Systems, Directed Graphs, FCT 2009, Theoretical Computer Science, Undirected Graphs