Computing the Tutte Polynomial on Graphs of Bounded Clique-Width

The Tutte polynomial is a notoriously hard graph invariant, and efficient algorithms for it are known only for a few special graph classes, like for those of bounded tree-width. The notion of clique-width extends the definition of cograhs (graphs without induced P4), and it is a more general notion than that of tree-width. We show a subexponential algorithm (running in time exp O(n1−ε ) ) for computing the Tutte polynomial on graphs of bounded clique-width. In fact, our algorithm computes the more general U-polynomial.

• Type: Conference
• Year: 2005
• Where: WG
• Authors: Omer Giménez, Petr Hlinený, Marc Noy
• Keywords: Computer Science, Hard Graph Invariant, Special Graph Classes, Tutte Polynomial, WG 2005