We study the atomic embeddability testing problem, which is a common generalization of
clustered planarity (c-planarity, for short) and thickenability testing, and present a polynomial …

For now almost 100 years, much attention has been devoted to studying embeddings of
complexes [8, 21, 32, 33, 43, 56, 68, 70]. Typical types of embeddings include geometric …

We introduce the problem Synchronized Planarity. Roughly speaking, its input is a loop-free
multi-graph together with synchronization constraints that, eg, match pairs of vertices of …

Firstly, we characterise the embeddability of simply connected locally 3-connected 2-
dimensional simplicial complexes in 3-space in a way analogous to Kuratowski's …

arXiv:1709.04643v3 [math.CO] 4 Sep 2019 Page 1 Embedding simply connected 2-complexes
in 3-space II. Rotation systems Johannes Carmesin University of Birmingham September 5 …

The game of Cops and Robber is usually played on a graph, where a group of cops attempt
to catch a robber moving along the edges of the graph. The cop number of a graph is the …

MULTIBRANCHED SURFACES IN 3-MANIFOLDS. - Document - Gale Academic OneFile Use
this link to get back to this page. Copy Skip to Content Library Menu: Google Scholar …

Hadwiger's conjecture, among the most famous open problems in graph theory, states that
every graph that does not contain K t as a minor is properly (t− 1)-colorable. The purpose of …

A simplicial complex is said to be {\em critical}(or {\em forbidden}) for the 3-sphere $ S^ 3$ if
it cannot be embedded in $ S^ 3$ but after removing any one point, it can be embedded. We …

We introduce the class of outerspatial 2-complexes as the natural generalisation of the class
of outerplanar graphs to three dimensions. Answering a question of O-joung Kwon, we …