The 2-layer drawing model is a well-established paradigm to visualize bipartite graphs. Several beyond-planar graph classes have been studied under this model. Surprisingly, however, the fundamental class of k-planar graphs has been considered only for k= 1 in this context. We provide several contributions that address this gap in the literature. First, we show tight density bounds for the classes of 2-layer k-planar graphs with k∈ { 2, 3, 4, 5 }. Based on these results, we provide a Crossing Lemma for 2-layer k-planar graphs, which then implies a general density bound for 2-layer k-planar graphs. We prove this bound to be almost optimal with a corresponding lower bound construction. Finally, we study relationships between k-planarity and h-quasiplanarity in the 2-layer model and show that 2-layer k-planar graphs have pathwidth at most k+ 1.
Angelini, P., Da Lozzo, G., Forster, H., & Schneck, T. (2020). 2-Layer k-Planar Graphs: Density, Crossing Lemma, Relationships, and Pathwidth. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp.403-419). Springer Science and Business Media Deutschland GmbH.
Titolo: | 2-Layer k-Planar Graphs: Density, Crossing Lemma, Relationships, and Pathwidth | |
Autori: | ||
Data di pubblicazione: | 2020 | |
Serie: | ||
Citazione: | Angelini, P., Da Lozzo, G., Forster, H., & Schneck, T. (2020). 2-Layer k-Planar Graphs: Density, Crossing Lemma, Relationships, and Pathwidth. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp.403-419). Springer Science and Business Media Deutschland GmbH. | |
Handle: | http://hdl.handle.net/11590/386171 | |
ISBN: | 978-3-030-68765-6 | |
Appare nelle tipologie: | 4.1 Contributo in Atti di convegno |