2015/10/08 by Therese Biedl, Thérèse Biedl, Biedl, Therese +2
Computer Science · Mathematics · #Advanced Image and Video Retrieval Techniques #Combinatorics (math.CO) #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #FOS: Mathematics #Graph Theory and Algorithms #cs.CG #math.CO
paper · pdf · doi:10.48550/arxiv.1510.02322
openalex publication_date 2015/10/08 · arxiv created 2015/10/12 · arxiv updated 2015/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well-known that every graph with maximum degree 4 has an orthogonal drawing with area at most (49)/(64) n2+O(n) ≈ 0.76n2. In this paper, we show that if the graph is 3-connected, then the area can be reduced even further to (9)/(16)n2+O(n) ≈ 0.56n2. The drawing uses the 3-canonical order for (not necessarily planar) 3-connected graphs, which is a special Mondshein sequence and can hence be computed in linear time. To our knowledge, this is the first application of a Mondshein sequence in graph drawing.