Abstract
We consider visibility representations of graphs in which the vertices are represented by a collection O of non-overlapping convex regions on the plane. Two points x and y are visible if the straight-line segment xy is not obstructed by any object. Two objects A, B ∈ O are called visible if there exist points x ∈ A, y ∈ B such that x is visible from y. We consider visibility only for a finite set of directions. In such a representation, the given graph is decomposed into a union of unidirectional visibility graphs, for the chosen set of directions. This raises the problem of studying the number of directions needed to represent a given graph. We study this number of directions as a graph parameter and obtain sharp upper and lower bounds for the represent ability of arbitrary graphs.
1980 Mathematics Subject Classification: 68R10, 68U05 CR Categories: F.2.2
Research supported in part by NSERC (Natural Sciences and Engineering Research Council of Canada) grant.
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© 1995 Springer-Verlag Berlin Heidelberg
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Kranakis, E., Krizanc, D., Urrutia, J. (1995). On the number of directions in visibility representations of graphs (extended abstract). In: Tamassia, R., Tollis, I.G. (eds) Graph Drawing. GD 1994. Lecture Notes in Computer Science, vol 894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58950-3_368
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DOI: https://doi.org/10.1007/3-540-58950-3_368
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