Unbent Collections of Orthogonal Drawings

Recently, there has been a lot of research around the idea of representing a single graph with multiple drawings, such that each drawing presents a certain part of the graph "nicely". For example, we may want a collection of drawings such that each edge is drawn with no crossings in at least one of the drawings, such collections are called uncrossed. Another example is the concept of graph storyplans, where we represent a graph by a collection of drawings of its subgraphs such that each vertex and edge of the graph is present in at least one drawing.

We consider the same principle idea in the language of orthogonal drawings. These are the drawings of plane 4-graphs in which each edge is represented by a sequence of vertical and horizontal line segments. We ask for a collection of orthogonal drawings of a graph G such that each edge is drawn with no bends in at least one of the drawings. Such a collection is called an unbent collection.

In this talk I will show a selection of combinatorial and algorithmic results around this new concept and discuss some possible directions for further research. Joint work with Giuseppe Liotta, Tomáš Masařík, Giacomo Ortali, Matthias Pfretzschner, Peter Stumpf, Alexander Wolff and Johannes Zink