Graphs with large total angular resolution

O. Aichholzer, M. Korman, Y. Okamoto, I. Parada, D. Perz, A. van Renssen, and B. Vogtenhuber

Abstract:

The total angular resolution of a straight-line drawing is the minimum angle between two edges of the drawing. It combines two properties contributing to the readability of a drawing: the angular resolution, which is the minimum angle between incident edges, and the crossing resolution, which is the minimum angle between crossing edges. We consider the total angular resolution of a graph, which is the maximum total angular resolution of a straight-line drawing of this graph. We prove tight bounds for the number of edges for graphs for some values of the total angular resolution up to a finite number of well specified exceptions of constant size. In addition, we show that deciding whether a graph has total angular resolution at least 60∘ is NP-hard. Further we present some special graphs and their total angular resolution.

Reference: O. Aichholzer, M. Korman, Y. Okamoto, I. Parada, D. Perz, A. van Renssen, and B. Vogtenhuber. Graphs with large total angular resolution. Theoretical Computer Science, 943:73-88, 2023.