max planck institut
informatik

# MPI-I-91-125

## Edge separators for graphs of bounded genus with applications

### Sýkora, Ondrej and Vrto, Imrich

MPI-I-91-125. November 1991, 10 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
$n$-vertex graph of positive genus $g$ and
maximal degree $k$ has an $O(\sqrt{gkn})$ edge separator. This bound
is best possible to within a constant factor. The separator can be
found in $O(g+n)$ time provided that we start with an imbedding
of the graph in its genus surface. This extends known results on
planar graphs and similar results about vertex separators.
We apply the edge
separator to the isoperimetric problem, to efficient embeddings of
graphs of genus $g$ into various classes of graphs including trees,
meshes and hypercubes and to showing lower bounds on crossing numbers
of $K_n,K_{m,n}$ and $Q_n$ drawn on surfaces of genus $g$.
Acknowledgement:
References to related material:

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BibTeX
@TECHREPORT{SykoraVrto91b
,
AUTHOR = {Sýkora, Ondrej and Vrto, Imrich},
TITLE = {Edge separators for graphs of bounded genus with applications},
TYPE = {Research Report},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},