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Two Maps on One Surface Dan Archdeacon
 

Summary: Two Maps on One Surface
Dan Archdeacon
Department of Mathematics and Statistics
University of Vermont
Burlington, VT, USA 05405
dan.archdeacon@uvm.edu
C. Paul Bonnington
Department of Mathematics
University of Auckland
Auckland, New Zealand
p.bonnington@auckland.ac.nz
Abstract
Two embeddings of a graph in a surface S are said to be \equiv-
alent" if they are identical under an homeomorphism of S that is
orientation-preserving for orientable S. Two graphs cellularly embed-
ded simultaneously in S are said to be \jointly embedded" if the only
points of intersection involve an edge of one graph transversally cross-
ing an edge of the other. The problem is to nd equivalent embeddings
of the two graphs that minimize the number of these edge-crossings;
this minimum we call the \joint crossing number" of the two graphs.

  

Source: Archdeacon, Dan - Department of Mathematics and Statistics, University of Vermont

 

Collections: Mathematics