Upward Book Embeddings of st-Graphs

03/19/2019
by   Carla Binucci, et al.
0

We study k-page upward book embeddings (kUBEs) of st-graphs, that is, book embeddings of single-source single-sink directed acyclic graphs on k pages with the additional requirement that the vertices of the graph appear in a topological ordering along the spine of the book. We show that testing whether a graph admits a kUBE is NP-complete for k≥ 3. A hardness result for this problem was previously known only for k = 6 [Heath and Pemmaraju, 1999]. Motivated by this negative result, we focus our attention on k=2. On the algorithmic side, we present polynomial-time algorithms for testing the existence of 2UBEs of planar st-graphs with branchwidth β and of plane st-graphs whose faces have a special structure. These algorithms run in O(f(β)· n+n^3) time and O(n) time, respectively, where f is a singly-exponential function on β. Moreover, on the combinatorial side, we present two notable families of plane st-graphs that always admit an embedding-preserving 2UBE.

READ FULL TEXT
research
04/16/2020

Four Pages Are Indeed Necessary for Planar Graphs

An embedding of a graph in a book consists of a linear order of its vert...
research
08/21/2020

Schematic Representation of Large Biconnected Graphs

Suppose that a biconnected graph is given, consisting of a large compone...
research
08/22/2017

Upward Partitioned Book Embeddings

We analyze a directed variation of the book embedding problem when the p...
research
03/17/2020

Book Embeddings of Nonplanar Graphs with Small Faces in Few Pages

An embedding of a graph in a book, called book embedding, consists of a ...
research
12/12/2020

Book Embeddings of k-Map Graphs

A map is a partition of the sphere into regions that are labeled as coun...
research
12/05/2013

Book embeddings of Reeb graphs

Let X be a simplicial complex with a piecewise linear function f:X→R. Th...
research
07/23/2019

Local and Union Page Numbers

We introduce the novel concepts of local and union book embeddings, and,...

Please sign up or login with your details

Forgot password? Click here to reset