Recognition algorithm for vertex-minors

Abstract

We show that for every fixed graph H with $l V(H) l \leqslant 6$, one can decide whether the input graph contains a vertex-minor isomorphic to H in polynomial time. To show this, we prove that for every graph H with $l V(H) l \leqslant 6$, graphs having no vertex-minor isomorphic to H have bounded rank-width, unless H is locally equivalent to the wheel graph on 6 vertices.