Finding small simple cycle separators for 2-connected planar graphs
Journal of Computer and System Sciences
Joint triangulations and triangulation maps
SCG '87 Proceedings of the third annual symposium on Computational geometry
Planar separators and the Euclidean norm
SIGAL '90 Proceedings of the international symposium on Algorithms
A Tura´n-type theorem on chords of a convex polygon
Journal of Combinatorial Theory Series B
On compatible triangulations of simple polygons
Computational Geometry: Theory and Applications
Some geometric applications of Dilworth's theorem
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Edge Separators for Planar Graphs and Their Applications
MFCS '88 Proceedings of the Mathematical Foundations of Computer Science 1988
Coloring kk-free intersection graphs of geometric objects in the plane
Proceedings of the twenty-fourth annual symposium on Computational geometry
Parameterized algorithmics for linear arrangement problems
Discrete Applied Mathematics
Coloring Kk-free intersection graphs of geometric objects in the plane
European Journal of Combinatorics
| Hi-index | 0.00 |
We show that any graph of n vertices that can be drawn in the plane with no k+1 pairwise crossing edges has at most cknlog2k−2n edges. This gives a partial answer to a dual version of a well-known problem of Avital-Hanani, Erdo&huml;s, Kupitz, Perles, and others. We also construct two point sets {p1,…,pn}, {q1,…,qn} in the plane such that any piecewise linear one-to-one mapping f:R2→R2 with f(pi)=qi (1≤i≤n) is composed of at least &OHgr;(n2) linear pieces. It follows from a recent result of Souvaine and Wenger that this bound is asymptotically tight. Both proofs are based on a relation between the crossing number and the bisection width of a graph.