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Stage-graph representations

✍ Scribed by Evangelos Kranakis; Danny Krizanc; Anil Maheshwari; Marc Noy; Jörg-Rüdiger Sack; Jorge Urrutia

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
634 KB
Volume
75
Category
Article
ISSN
0166-218X

No coin nor oath required. For personal study only.

✦ Synopsis

We consider graph applications of the well-known paradigm "killing two birds with one stone". In the plane, this gives rise to a stage graph as follows: vertices are the points, and {u, II} is an edge if and only if the (infinite, straight) line segment joining u to u intersects the stage. Such graphs are shown to be comparability graphs of ordered sets of dimension 2. Similar graphs can be constructed when we have a fixed number k of stages on the plane. In this case, {u, u} is an edge if and only if the (straight) line segment uu intersects one of the k stages. In this paper, we study stage representations of stage graphs and give upper and lower bounds on the number of stages needed to represent a graph.

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