Thread Graphs, Linear Rank-Width and Their Algorithmic Applications
The introduction of tree-width by Robertson and Seymour  was a breakthrough in the design of graph algorithms. A lot of research since then has focused on obtaining a width measure which would be more general and still allowed efficient algorithms for a wide range of NP-hard problems on graphs of bounded width. To this end, Oum and Seymour have proposed rank-width, which allows the solution of many such hard problems on a less restricted graph classes (see e.g. [3,4]). But what about problems which are NP-hard even on graphs of bounded tree-width or even on trees? The parameter used most often for these exceptionally hard problems is path-width, however it is extremely restrictive – for example the graphs of path-width 1 are exactly paths.
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- 2.Ganian, R.: Thread graphs, linear rank-width and their algorithmic applications (manuscript), http://is.muni.cz/www/99352/threadgraphs.pdf
- 4.Ganian, R., Hliněný, P.: On parse trees and Myhill–Nerode–type tools for handling graphs of bounded rank-width. Discrete Appl. Math. (2009) (to appear)Google Scholar