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.
Graph isomorphisms in quasi-polynomial time
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Let us be given two graphs $\Gamma_1$, $\Gamma_2$ of $n$ vertices. Are they isomorphic? If they are, the set of isomorphisms from $\Gamma_1$ to $\Gamma_2$ can be identified with a coset $H\cdot\pi$ inside the symmetric group on $n$ elements. How do we find $\pi$ and a set of generators of $H$? The challenge of giving an always efficient algorithm answering these questions remained open for a long time. Babai has recently shown how to solve these problems -- and others linked to them -- in quasi-polynomial time, i.e. in time $\exp\left(O(\log n)^{O(1)}\right)$. His strategy is based in part on the algorithm by Luks (1980/82), who solved the case of graphs of bounded degree.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Any circulant ternary coherent configuration of prime degree p is schurian, except possibly when it is an association scheme on triples with Aut(X) equal to AGL1(p) for p ≡ ±1 mod 8 or a proper subgroup thereof.
citing papers explorer
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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.
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On circulant ternary coherent configurations of prime degree
Any circulant ternary coherent configuration of prime degree p is schurian, except possibly when it is an association scheme on triples with Aut(X) equal to AGL1(p) for p ≡ ±1 mod 8 or a proper subgroup thereof.