Abstract
The dominance drawing method has many important aesthetic properties, including small number of bends, good vertex placement, and symmetry display [1]. Furthermore, it encapsulates the aspect of characterizing the transitive closure of the digraph by means of a geometric dominance relation among the vertices. A dominance drawing Γ of a planar st-graph G is a drawing, such that for any two vertices u and v there is a directed path from u to v in G if and only if X(u) ≤ X(v) and Y(u) ≤ Y(v) in Γ [1]. Here we study weak dominance drawings where for any two vertices u and v if there is a directed path from u to v in G then X(u) ≤ X(v) and Y(u) ≤ Y(v) in Γ.
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References
Di Battista, G., Tamassia, R., Tollis, I.G.: Area Requirement and Symmetry Display of Planar Upward Drawings. Discrete and Comput. Geom. 7(4), 381–401 (1992)
Eades, P., ElGindy, H., Houle, M., Lenhart, B., Miller, M., Rappaport, D., Whitesides, S.: Dominance Drawings of Bipartite Graphs (1993) (manuscript)
Kornaropoulos, E.M., Tollis, I.G.: Weak Dominance Drawings and Linear Extension Diameter, arXiv:1108.1439 (2011)
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Kornaropoulos, E.M., Tollis, I.G. (2013). Weak Dominance Drawings for Directed Acyclic Graphs. In: Didimo, W., Patrignani, M. (eds) Graph Drawing. GD 2012. Lecture Notes in Computer Science, vol 7704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36763-2_52
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DOI: https://doi.org/10.1007/978-3-642-36763-2_52
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