Convex obstacle numbers of outerplanar graphs and bipartite permutation graphs
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 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2011
 arXiv:
 arXiv:1104.4656
 Bibcode:
 2011arXiv1104.4656F
 Keywords:

 Computer Science  Discrete Mathematics;
 Computer Science  Computational Geometry;
 Mathematics  Combinatorics;
 68R10;
 05C10;
 05C62;
 F.2.2;
 G.2.2
 EPrint:
 11 pages, 6 figures