Convex Obstacle Numbers of Outerplanar Graphs and Bipartite Permutation Graphs

Radoslav Fulek (), Noushin Saeedi () and Deniz Sarıöz ()
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Radoslav Fulek: École Polytechnique Fédérale de Lausanne
Noushin Saeedi: The University of British Columbia
Deniz Sarıöz: The Graduate School and University Center of The City University of New York

A chapter in Thirty Essays on Geometric Graph Theory, 2013, pp 249-261 from Springer

Abstract: Abstract The disjoint convex obstacle number of a graph G is the smallest number h such that there is a set of h pairwise disjoint convex polygons (obstacles) and a set of n points in the plane [corresponding to V (G))]so that a vertex pair uv is an edge if and only if the corresponding segment $$\overline{uv}$$ does not meet any obstacle. We show that the disjoint convex obstacle number of an outerplanar graph is always at most 5, and of a bipartite permutation graph at most 4. The former answers a question raised by Alpert, Koch, and Laison. We complement the upper bound for outerplanar graphs with the lower bound of 4.

Keywords: Outerplanar Graph; Permutation Graph; Obstacle Representation; Vertical Line Segment; Extra Edge (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-0110-0_13

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DOI: 10.1007/978-1-4614-0110-0_13

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