This paper presents an empirical study of the relationship between the density of small-medium sized random graphs and their planarity. It is well known that, when the number of vertices tends to infinite, there is a sharp transition between planarity and non-planarity for edge density d=0.5. However, this asymptotic property does not clarify what happens for graphs of reduced size. We show that an unexpectedly sharp transition is also exhibited by small and medium sized graphs. Also, we show that the same “tipping point” behavior can be observed for some restrictions or relaxations of planarity (we considered outerplanarity and near-planarity, respectively).
Balloni, E., Di Battista, G., Patrignani, M. (2020). A Tipping Point for the Planarity of Small and Medium Sized Graphs. In Graph Drawing and Network Visualization 28th International Symposium, GD 2020 (pp.181-188). Springer [10.1007/978-3-030-68766-3_15].
A Tipping Point for the Planarity of Small and Medium Sized Graphs
Di Battista, Giuseppe;Patrignani, Maurizio
2020-01-01
Abstract
This paper presents an empirical study of the relationship between the density of small-medium sized random graphs and their planarity. It is well known that, when the number of vertices tends to infinite, there is a sharp transition between planarity and non-planarity for edge density d=0.5. However, this asymptotic property does not clarify what happens for graphs of reduced size. We show that an unexpectedly sharp transition is also exhibited by small and medium sized graphs. Also, we show that the same “tipping point” behavior can be observed for some restrictions or relaxations of planarity (we considered outerplanarity and near-planarity, respectively).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
