Introduces the k-Tinhofer hierarchy between general graphs and Tinhofer graphs, gives algebraic and combinatorial characterizations, proves strict separations for each k, shows P-hardness of deciding membership in the next level, and proves FPT isomorphism testing for (n-k)-Tinhofer graphs.
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A Hierarchy of Tinhofer Graphs: Separations and Membership Testing
Introduces the k-Tinhofer hierarchy between general graphs and Tinhofer graphs, gives algebraic and combinatorial characterizations, proves strict separations for each k, shows P-hardness of deciding membership in the next level, and proves FPT isomorphism testing for (n-k)-Tinhofer graphs.