The recently introduced twin-width of a graph G is the minimum integer d such that G has a d-
contraction sequence, that is, a sequence of| V (G)|–1 iterated vertex identifications for which …

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 …

We show that there exists an adjacency labelling scheme for planar graphs where each
vertex of an n-vertex planar graph G is assigned a (1+ o (1)) log 2 n-bit label and the labels …

This survey article is devoted to general results in combinatorial enumeration. The first part
surveys results on growth of hereditary properties of combinatorial structures. These include …

Twin-width is a recently introduced graph parameter with applications in algorithmics,
combinatorics, and finite model theory. For graphs of bounded degree, finiteness of twin …

A conjecture in algorithmic model theory predicts that the model-checking problem for first-
order logic is fixed-parameter tractable on a hereditary graph class if and only if the class is …

A clique is a set of pairwise adjacent vertices in a graph. We determine the maximum
number of cliques in a graph for the following graph classes:(1) graphs with n vertices and m …

This text is aimed at doctoral students and researchers, who are interested in Combinatorics
and Graph Theory or who would just like to learn about some active topics and trends. But …

List Colouring Squares of Planar Graphs Page 1 List Colouring Squares of Planar Graphs
Frédéric Haveta,1, Jan van den Heuvelb,1, Colin McDiarmidc,1, and Bruce Reedd,1 a …

A string graph is the intersection graph of a collection of continuous arcs in the plane. We
show that any string graph with m edges can be separated into two parts of roughly equal …