Abstract
Arc-connected sets A, B ⊂E 2 are called noncrossing if both A-B and B-A are arc-connected. A graph is called an NCAC graph if it has an intersection representation in which vertices are represented by arc-connected sets in the plane and any two sets of the representation are noncrossing. In particular, disk intersection graphs are NCAC. By a unified reduction we show that recognition of disk intersection and NCAC graphs are NP-hard. A simple observation shows that triangle-free disk intersection and NCAC graphs are planar, and hence recognizable in polynomial time. On the other hand, recognition of triangle-free AC graphs (intersection graphs of arc-connected sets) is still NP-hard.
The author acknowledges partial support of Czech Research grants GA ČR 0194 and GA UK 193 and of Czech-US Science and Technology Research grant No. 94 051.
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Kratochvíl, J. (1997). Intersection graphs of noncrossing arc-connected sets in the plane. In: North, S. (eds) Graph Drawing. GD 1996. Lecture Notes in Computer Science, vol 1190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62495-3_53
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DOI: https://doi.org/10.1007/3-540-62495-3_53
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