Interval Visibility Graphs

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Consider a vertical stack of open intervals, such as , , , . Two intervals are said to have vertical visibility if a vertical line can be drawn between two intervals without intersecting some other interval.


Graphs can represent interval visibility by mapping horizontal intervals to vertices and vertical lines to edges. All such graphs must be planar.

These are frequently called bar visibility graphs.


Contributed by: Ed Pegg Jr (September 2015)
Open content licensed under CC BY-NC-SA




[1] Y. Chang, J. P. Hutchinson, M. S. Jacobson, J. Lehel, D. B. West, "The Bar Visibility Number of a Graph," SIAM Journal on Discrete Mathematics, 18(3), 2004, pp. 462–471.

[2] M. Axenovich, A. Beveridge, J. P. Hutchinson, and D. B. West, "Visibility Number of Directed Graphs," SIAM Journal on Discrete Mathematics, 27(3), 2013 pp. 1429–1449.

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