Unbent Collections of Orthogonal Drawings
Todor Anti\'c, Giuseppe Liotta, Tom\'a\v{s} Masa\v{r}\'ik, Giacomo Ortali, Matthias Pfretzschner, Peter Stumpf, Alexander Wolff, Johannes Zink

TL;DR
This paper explores representing plane 4-graphs with collections of orthogonal drawings, ensuring each edge is bend-free in at least one drawing, and provides bounds, conditions, and algorithms for optimal collections.
Contribution
It establishes tight bounds on the number of drawings needed and characterizes graphs with minimal unbent collections, along with algorithms for minimizing total bends.
Findings
Every plane 4-graph can be represented by at most three drawings.
Necessary and sufficient conditions for unbent collections of size 2 are provided.
Minimizing total bends is NP-hard; a 3-approximation algorithm is proposed.
Abstract
Recently, there has been interest in representing single graphs by multiple drawings; for example, using graph stories, storyplans, or uncrossed collections. In this paper, we apply this idea to orthogonal graph drawing. Due to the orthogonal drawing style, we focus on 4-graphs, that is, graphs of maximum degree 4. We restrict ourselves to plane graphs, that is, planar graphs whose embedding is fixed. Our goal is to represent any plane 4-graph by an unbent collection, that is, a collection of orthogonal drawings of that adhere to the embedding of and ensure that each edge of is drawn without bends in at least one of the drawings. We investigate two objectives. First, we consider minimizing the number of drawings in an unbent collection. We prove that every plane 4-graph can be represented by a collection with at most three drawings, which is tight. We also give necessary…
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