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On the Crossing Number of Complete Graphs (Extended Abstract)
 

Summary: On the Crossing Number of Complete Graphs
(Extended Abstract)
Oswin Aichholzer  Franz Aurenhammer Hannes Krasser y
Institute for Theoretical Computer Science
Graz University of Technology
Graz, Austria
foaich,auren,hkrasserg@igi.tu-graz.ac.at
ABSTRACT
We determine cr(K11) = 102 and cr(K12 ) = 153. Moreover,
we give improved upper and lower bounds on the asymptotic
saving of crossings when drawing Kn optimally.
Categories and Subject Descriptors
G.2.1 [Mathematics of Computing]: Discrete Mathe-
matics|Combinatorics, Counting problems; F.2.2 [Non-
numerical Algorithms]: Geometric problems and compu-
tations|computations on discrete structures
Keywords
Rectilinear crossing number, complete graph, order type
1. INTRODUCTION
The crossing number of a graph G is the least number of

  

Source: Aurenhammer, Franz - Institute for Theoretical Computer Science, Technische Universitšt Graz
Krasser, Hannes - Institute for Theoretical Computer Science, Technische Universitšt Graz
Technische Universitšt Graz, Institute for Software Technology

 

Collections: Computer Technologies and Information Sciences