Let GH(S; H) be the bipartite graph with partition sets S and H , the set of simplices and hyperplanes of H, where simplex s∈ S is adjacent to hyperplane h∈H if one facet of s lies on h. In this paper, we give a complete characterization of GH(S; H) when H is a -arrangement. We also study GH(S; H) when H is a pseudoline arrangement. c © 2001 Elsevier Science B.V. All rights reserved.

In various research papers, such as [2], one will find the claim that the minLA is optimally solvable on outerplanar graphs, with a reference to [1]. However, the problem solved in that publication, which we refer to as the planar minLA, is different from the minLA, as we show in this article. In constrast to the minimum linear arrangement problem (minLA), the planar minimum linear arrangement ...

Any finite set of lines in the real projective plane determines a cell complex; these complexes and their combinatorial properties have been a subject of study at least since 1826 [9]. More recently, Levi [6] considered a topological generalization of this notion, defined as follows: Consider a simple closed curve in RP2 which does not separate RP2; this is called a pseudoline. (It is clear tha...

We introduce a new combinatorial object, the double-permutation sequence, and use it to encode a family of mutually disjoint compact convex sets in the plane in a way that captures many of its combinatorial properties. We use this encoding to give a new proof of the Edelsbrunner-Sharir theorem that a collection of n compact convex sets in the plane cannot be met by straight lines in more than 2...

We discuss different variants of linear arrangement problems from a parameterized perspective. More specifically, we concentrate on developing simple search tree algorithms for these problems. However, the analysis of these algorithms is sometimes not so easy.

1 Contributions from the Bermuda Biological Station for Research, No. 113. 2 Crozier, W. J., and Arey, L. B., " Sensory reactions of Chromodoris zebra," J. Exper. Zool., Phila., (in press). 3 Crozier, W. J., 1919, J. Gen. Physiol., Baltimore, 1, No. 6. 4 For more detailed treatment of the complex conditions here entering, consult papers cited in footnotes two and three. 6 cf. Parker, G. H., 191...