The graph crossing number and its variants: A survey

M Schaefer - The electronic journal of combinatorics, 2012 - combinatorics.org
The crossing number is a popular tool in graph drawing and visualization, but there is not
really just one crossing number; there is a large family of crossing number notions of which …

Four pages are indeed necessary for planar graphs

MA Bekos, M Kaufmann, F Klute, S Pupyrev… - arxiv preprint arxiv …, 2020 - arxiv.org
An embedding of a graph in a book consists of a linear order of its vertices along the spine of
the book and of an assignment of its edges to the pages of the book, so that no two edges on …

[HTML][HTML] Book embeddings of k-framed graphs and k-map graphs

MA Bekos, G Da Lozzo, SM Griesbach… - Discrete …, 2024 - Elsevier
An embedding of a graph in a book, called book embedding, consists of a linear ordering of
its vertices along the spine of the book and an assignment of its edges to the pages of the …

Book embeddings of nonplanar graphs with small faces in few pages

MA Bekos, G Da Lozzo, S Griesbach… - arxiv preprint arxiv …, 2020 - arxiv.org
An embedding of a graph in a book, called book embedding, consists of a linear ordering of
its vertices along the spine of the book and an assignment of its edges to the pages of the …

Upward book embeddings of st-graphs

C Binucci, G Da Lozzo, E Di Giacomo… - arxiv preprint arxiv …, 2019 - arxiv.org
We study $ k $-page upward book embeddings ($ k $ UBEs) of $ st $-graphs, that is, book
embeddings of single-source single-sink directed acyclic graphs on $ k $ pages with the …

The book thickness of 1-planar graphs is constant

MA Bekos, T Bruckdorfer, M Kaufmann… - Algorithmica, 2017 - Springer
In a book embedding, the vertices of a graph are placed on the “spine” of a book and the
edges are assigned to “pages”, so that edges on the same page do not cross. In this paper …

Parameterized algorithms for book embedding problems

S Bhore, R Ganian, F Montecchiani… - Journal of Graph …, 2020 - jgaa.info
A $ k $-page book embedding of a graph $ G $ draws the vertices of $ G $ on a line and the
edges on $ k $ half-planes (called pages) bounded by this line, such that no two edges on …

[HTML][HTML] Recognizing DAGs with page-number 2 is NP-complete

MA Bekos, G Da Lozzo, F Frati, M Gronemann… - Theoretical Computer …, 2023 - Elsevier
The page-number of a directed acyclic graph (a DAG, for short) is the minimum k for which
the DAG has a topological order and a k-coloring of its edges such that no two edges of the …

On dispersable book embeddings

JM Alam, MA Bekos, V Dujmović, M Gronemann… - Theoretical Computer …, 2021 - Elsevier
In a dispersable book embedding, the vertices of a given graph G must be ordered along a
line ℓ, called spine, and the edges of G must be drawn in different half-planes bounded by ℓ …

Triconnected planar graphs of maximum degree five are subhamiltonian

M Hoffmann, B Klemz - 27th Annual European Symposium on …, 2019 - drops.dagstuhl.de
We show that every triconnected planar graph of maximum degree five is subhamiltonian
planar. A graph is subhamiltonian planar if it is a subgraph of a Hamiltonian planar graph or …