Linear rank-width and linear clique-width of trees

Isolde Adler, Mamadou Moustapha Kanté
2015 Theoretical Computer Science  
We show that for every forest T the linear rank-width of T is equal to the path-width of T , and the linear clique-width of T equals the path-width of T plus two, provided that T contains a path of length three. It follows that both linear rank-width and linear clique-width of forests can be computed in linear time. Using our characterization of linear rank-width of forests, we determine the set of minimal excluded acyclic vertex-minors for the class of graphs of linear rank-width at most k.
doi:10.1016/j.tcs.2015.04.021 fatcat:vehu66rrfbfdfkwhnzs75u66km