The graph isomorphism problem Page 1 128 COMMUNICATIONS OF THE ACM |
NOVEMBER 2020 | VOL. 63 | NO. 11 review articles IMA GE B Y NAD A V/SHUTTERS T …

This paper investigates ultrafilters in the context of connectivity systems, defined as pairs (X,
f) where X is a finite set and f is a symmetric submodular function. Ultrafilters, essential in …

We give an algorithm that for an input n-vertex graph G and integer k>0, in time 2^O(k)n,
either outputs that the treewidth of G is larger than k, or gives a tree decomposition of G of …

We generalize the structure theorem of Robertson and Seymour for graphs excluding a fixed
graph H as a minor to graphs excluding H as a topological subgraph. We prove that for a …

The group isomorphism problem determines whether two groups, given by their Cayley
tables, are isomorphic. For groups with order n, an algorithm with n (log n+ O (1)) running …

We prove that the combinatorial Weisfeiler-Leman algorithm of dimension (3 k+ 4) is a
complete isomorphism test for the class of all graphs of rank width at most k. Rank width is a …

In a recent breakthrough, Babai Proceedings of STOC, ACM, New York, 2016, pp. 684--697
gave a quasipolynomial-time graph isomorphism test. In this work, we give an improved …

We give an algorithm that, for every fixed k, decides isomorphism of graphs of rank width at
most k in polynomial time. As the rank width of a graph is bounded in terms of its clique …

A commonly studied means of parameterizing graph problems is the deletion distance from
triviality (Guo et al., Parameterized and exact computation, Springer, Berlin, pp. 162–173 …

We give a new FPT algorithm testing isomorphism of n-vertex graphs of tree-width k in time 2
kpolylog (k) n3, improving the FPT algorithm due to Lokshtanov, Pilipczuk, Pilipczuk, and …