The study of graph structure has advanced in recent years with great strides: finite graphs
can be described algebraically, enabling them to be constructed out of more basic elements …

A contraction sequence of a graph consists of iteratively merging two of its vertices until only
one vertex remains. The recently introduced twin-width graph invariant is based on …

Branchwidth determines how graphs, and more generally, arbitrary connectivity (basically
symmetric and submodular) functions could be decomposed into a tree-like structure by …

In this survey, we review practical algorithms for graph-theoretic problems that are
expressible in monadic second-order logic. Monadic second-order (MSO) logic allows …

We introduce the graph parameter boolean-width, related to the number of different unions
of neighborhoods–Boolean sums of neighborhoods–across a cut of a graph. For many …

Parameterized algorithms are often used to efficiently solve NP-hard problems on graphs. In
this context, vertex cover is used as a powerful parameter for dealing with graph problems …

A proof-labeling scheme (PLS) for a boolean predicate $\Pi $ on labeled graphs is a
mechanism used for certifying the legality with respect to $\Pi $ of global network states in a …

Stabilizer states form an important class of states in quantum information, and are of central
importance in quantum error correction. Here, we provide an algorithm for deciding whether …

We develop a framework for applying treewidth-based dynamic programming on graphs
with “hybrid structure”, ie, with parts that may not have small treewidth but instead possess …

Tree-cut width is a parameter that has been introduced as an attempt to obtain an analogue
of treewidth for edge cuts. Unfortunately, in spite of its desirable structural properties, it …