Square roots of minor closed graph classes
Let G G be a graph class. The square root  of G G contains all graphs whose squares belong in G G . We prove that if G G is non-trivial and minor closed, then all graphs in its square root have carving-width bounded by some constant depending only on G G . As a consequence, every square root of such a graph class has a linear time recognition algorithm.
carving-width square roots of graphs branch-width graph minors