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A note on visibility graphs

✍ Scribed by F Luccio; S Mazzone; C.K Wong

Publisher: Elsevier Science
Year: 1987
Tongue: English
Weight: 602 KB
Volume: 64
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(87)90190-7

No coin nor oath required. For personal study only.

✦ Synopsis

Given a set S = {s 1, s 2, ..., s,,) of vertical line segments, si, sj see each other ff there is a horizontal line segment which intersects them, but does not intersect any other line segment between them.

A ws" ibility graph G of vertices {vl, v2, • .., v,,} is put into a one-to-one correspondence with S, such that s/corresponds to vi, and edge {v i, v/} exists in G iff si, sj see each other.

We prove that any visibility graph G is ipo-triangular, that is, it can be transformed into a planar multigraph with all triangular finite faces, by successive duplications of existing edges of G. Conversely we prove that any ipo-triangular graph is a visibility graph for some set S.

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