Department of Computer Science | Institute of Theoretical Computer Science | CADMO
Theory of Combinatorial Algorithms
Prof. Emo Welzl and Prof. Bernd Gärtner
Department of Computer Science | Institute of Theoretical Computer Science | CADMO
Prof. Emo Welzl and Prof. Bernd Gärtner
| Mittagsseminar Talk Information |
Date and Time: Tuesday, February 18, 2025, 12:15 pm
Duration: 30 minutes
Location: CAB G51
Speaker: Michael Hoffmann
Arc diagrams are plane embeddings of graphs that represent vertices as points on a horizontal line, called spine, and each edge as a sequence of halfcircles centered on the spine. If each such sequence consists of one halfcircle only, then we face a 2-page book embedding. Not every planar graph admits a 2-page book embedding, only the subgraphs of Hamiltonian planar graphs do. But every planar graph admits an arc diagram where each edge is represented as a sequence of two halfcircles, a so-called biarc. Furthermore, we can restrict all biarcs to be monotone with respect to the spine. Some number of edges can always be represented as proper arcs, that is, as a single halfcircle. But how many? For a planar graph G, let mhd(G) denote the minimum number of biarcs over all arc diagrams of G where each edge is represented as a proper arc or as a monotone biarc. In this talk I will discuss upper and lower bounds on mhd for some classes of planar graphs. This is joint work with Steven Chaplick, Henry Förster, and Michael Kaufmann.
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