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 …

A sublinear bound on the page number of upward planar graphs

P Jungeblut, L Merker, T Ueckerdt - SIAM Journal on Discrete Mathematics, 2023 - SIAM
The page number of a directed acyclic graph is the minimum for which there is a topological
ordering of and a-coloring of the edges such that no two edges of the same color cross, ie …

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 …

[HTML][HTML] On the upward book thickness problem: combinatorial and complexity results

S Bhore, G Da Lozzo, F Montecchiani… - European Journal of …, 2023 - Elsevier
Among the vast literature concerning graph drawing and graph theory, linear layouts of
graphs have been the subject of intense research over the years, both from a combinatorial …

[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 …

[HTML][HTML] Extending upward planar graph drawings

G Da Lozzo, G Di Battista, F Frati - Computational Geometry, 2020 - Elsevier
In this paper we study the computational complexity of the Upward Planarity Extension
problem, which takes as input an upward planar drawing Γ H of a subgraph H of a directed …

On upward-planar L-drawings of graphs

P Angelini, S Chaplick, S Cornelsen… - arXiv preprint arXiv …, 2022 - arxiv.org
In an upward-planar L-drawing of a directed acyclic graph (DAG) each edge $ e $ is
represented as a polyline composed of a vertical segment with its lowest endpoint at the tail …

On the upward book thickness problem: Combinatorial and complexity results

S Bhore, G Da Lozzo, F Montecchiani… - … Symposium on Graph …, 2021 - Springer
A long-standing conjecture by Heath, Pemmaraju, and Trenk states that the upward book
thickness of outerplanar DAGs is bounded above by a constant. In this paper, we show that …

Upward Book Embeddability of st-Graphs: Complexity and Algorithms

C Binucci, G Da Lozzo, E Di Giacomo, W Didimo… - Algorithmica, 2023 - Springer
A k-page upward book embedding (k UBE) of a directed acyclic graph G is a book
embeddings of G on k pages with the additional requirement that the vertices appear in a …