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 …

Graph neural networks are prominent models for representation learning over graphs,
where the idea is to iteratively compute representations of nodes of an input graph through a …

We prove that the Weisfeiler--Leman (WL) dimension of the class of all finite planar graphs is
at most 3. In particular, every finite planar graph is definable in first-order logic with counting …

Abstract The Weisfeiler-Leman (WL) algorithm is a fundamental combinatorial technique
used to classify graphs and other relational structures. It dates back to the 1960s and has …

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 …

Graph embeddings of bounded Euler genus (that means, embeddings with bounded
orientable or nonorientable genus) help to design time-efficient algorithms for many graph …

Graph canonization is the problem of computing a unique representative, a canon, from the
isomorphism class of a given graph. This implies that two graphs are isomorphic exactly if …

We present a logspace algorithm for computing a canonical labeling, in fact, a canonical
interval representation, for interval graphs. To achieve this, we compute canonical interval …

We obtain the following new simultaneous time-space upper bounds for the directed
reachability problem.(1) A polynomial-time, O (n^{2/3}* g^{1/3})-space algorithm for directed …

Counting the number of perfect matchings in graphs is a computationally hard problem.
However, in the case of planar graphs, and even for K 3, 3-free graphs, the number of …