Graph Drawing Beyond Planarity is a rapidly growing research area that classifies and
studies geometric representations of nonplanar graphs in terms of forbidden crossing …

The notion of 1-planarity is among the most natural and most studied generalizations of
graph planarity. A graph is 1-planar if it has an embedding where each edge is crossed by at …

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 show that planar graphs have bounded queue-number, thus proving a conjecture of
Heath et al.[66] from 1992. The key to the proof is a new structural tool called layered …

Hadwiger's Conjecture asserts that every K_h-minor-free graph is properly (h-1)-colourable.
We prove the following improper analogue of Hadwiger's Conjecture: for fixed h, every K_h …

Consider the following two ways to colour the vertices of a graph where the requirement that
adjacent vertices get distinct colours is relaxed. A colouring has" defect" $ d $ if each …

We consider relations between the size, treewidth, and local crossing number (maximum
number of crossings per edge) of graphs embedded on topological surfaces. We show that …

The planar graph product structure theorem of Dujmović et al.[J. ACM, 67 (2020), 22] states
that every planar graph is a subgraph of the strong product of a graph with bounded …

The asymptotic dimension is an invariant of metric spaces introduced by Gromov in the
context of geometric group theory. In this paper, we study the asymptotic dimension of metric …

Hadwiger's conjecture asserts that every K t‐minor‐free graph has a proper (t− 1)‐colouring.
We relax the conclusion in Hadwiger's conjecture via improper colourings. We prove that …