6 citations · 10 across the 7 of their papers we have counts for
11 papers · 1 filter
Separating Geodesic Structure and Product Structure
Laura Merker, Lena Scherzer, Samuel Schneider
The geodesic treewidth of a graph is the smallest for which there is a partition into geodesics such that has treewidth , where $G/\mathc…
Product Structure and Treewidth of Hyperbolic Uniform Disk Graphs
Thomas Bläsius, Emil Dohse, Deborah Haun +1
Hyperbolic uniform disk graphs (HUDGs) are intersection graphs of disks with some radius in the hyperbolic plane, where may be constant or depend on the number of vertices…
Intersection Graphs with and without Product Structure
Laura Merker, Lena Scherzer, Samuel Schneider +1
A graph class admits product structure if there exists a constant such that every is a subgraph of for a path and some gra…
Linear Layouts of Bipartite Planar Graphs
Henry Förster, Michael Kaufmann, Laura Merker +2
A linear layout of a graph consists of a linear order of the vertices and a partition of the edges. A part is called a queue (stack) if no two edges nest (cross), tha…
Directed Acyclic Outerplanar Graphs Have Constant Stack Number
Paul Jungeblut, Laura Merker, Torsten Ueckerdt
The stack 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 s…
The product structure of squaregraphs
Robert Hickingbotham, Paul Jungeblut, Laura Merker +1
A squaregraph is a plane graph in which each internal face is a -cycle and each internal vertex has degree at least 4. This paper proves that every squaregraph is isomorphic to…
Three-dimensional graph products with unbounded stack-number
David Eppstein, Robert Hickingbotham, Laura Merker +3
We prove that the stack-number of the strong product of three -vertex paths is . The best previously known upper bound was . No non-trivial lower bound was kno…
Linear Layouts of Complete Graphs
Stefan Felsner, Laura Merker, Torsten Ueckerdt +1
A page (queue) with respect to a vertex ordering of a graph is a set of edges such that no two edges cross (nest), i.e., have their endpoints ordered in an ABAB-pattern (ABBA-patte…
A Sublinear Bound on the Page Number of Upward Planar Graphs
Paul Jungeblut, Laura Merker, Torsten Ueckerdt
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 sa…
The Local Queue Number of Graphs with Bounded Treewidth
Laura Merker, Torsten Ueckerdt
A queue layout of a graph consists of a vertex ordering of and a partition of the edges into so-called queues such that no two edges in the same queue nest, i.e., have thei…
Local and Union Page Numbers
Laura Merker, Torsten Ueckerdt
We introduce the novel concepts of local and union book embeddings, and, as the corresponding graph parameters, the local page number and the union page number $…