COMPUTATION OF LINEAR RANK-WIDTH Keywords: linear rank-width; rank-decomposition; path-decomposition; vertex-minor Internship at Limos, Clermont-Ferrand, supervised by

(1) It is equivalent to clique-width, a complexity measure introduced by Courcelle et al. [4], that generalises the well-known complexity measure tree-width introduced by Robertson and Seymour in their graph minors series. (2) It is algorithmically more interesting than clique-width because we can recognise in polynomial time graphs of rank-width at most k (for fixed k) (3) It shares with tree-width many structural properties (its is for instance related to the theory of matroids and is related to the vertexminor relation [6]). (4) . . .