On the OBDD Size for Graphs of Bounded Tree- and Clique-Width

We study the size of OBDDs (ordered binary decision diagrams) for representing the adjacency function fG of a graph G on n vertices. Our results are as follows: for graphs of bounded tree-width there is an OBDD of size O(logn) for fG that uses encodings of size O(logn) for the vertices; for graphs of bounded clique-width there is an OBDD of size O(n) for fG that uses encodings of size O(n) for the vertices; for graphs of bounded clique-width such that there is a reduced term for G (to be defined below) that is balanced with depth O(logn) there is an OBDD of size O(n) for fG that uses encodings of size O(logn) for the vertices; for cographs, i.e. graphs of clique-width at most 2, there is an OBDD of size O(n) for fG that uses encodings of size O(logn) for the vertices. This last result improves a recent result by Nunkesser and Woelfel [14].