Color refinement is a classical technique used to show that two given graphs $G$ and $H$
are non-isomorphic; it is very efficient, although it does not succeed on all graphs. We call a graph $G$ amenable to color refinement if the color-refinement procedure succeeds in distinguishing $G$ from any non-isomorphic ... more >>>

In this paper we study the complexity of factorization of polynomials in the free noncommutative ring $\mathbb{F}\langle x_1,x_2,\ldots,x_n\rangle$ of polynomials over the field $\mathbb{F}$ and noncommuting variables $x_1,x_2,\ldots,x_n$. Our main results are the following.

Although $\mathbb{F}\langle x_1,\dots,x_n \rangle$ is not a unique factorization ring, we note that variable-disjoint factorization in ... more >>>

We give a $O^*(k^{O(k)})$ time isomorphism testing algorithm for graphs of eigenvalue multiplicity bounded by $k$ which improves on the previous
best running time bound of $O^*(2^{O(k^2/\log
k)})$.

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We study the complexity of Geometric Graph Isomorphism, in
$l_2$ and other $l_p$ metrics: given two sets of $n$ points $A,
B\subset \mathbb{Q}^k$ in
$k$-dimensional euclidean space the problem is to
decide if there is a bijection $\pi:A \rightarrow B$ such that for
... more >>>