2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 45-50
| author: | Bruce Reed and David R. Wood |
|---|---|
| title: | Fast separation in a graph with an excluded minor |
| keywords: | graph algorithm, separator, minor |
| abstract: |
Let
G
be an
n
-vertex
m
-edge graph with weighted vertices. A pair of vertex
sets
A,B⊆V(G)
is a 2/3-separation of order
|A∩B|
if
A ∪B = V(G)
, there is no edge between
A \ B
and
B \ A
, and both
A \ B
and
B \ A
have weight at most
2/3
the total weight of
G
. Let
ℓ∈ℤ+
be fixed. Alon, Seymour and Thomas
[J. Amer. Math. Soc. 1990]
presented an algorithm that in
O
(n
1/2
m)
K
-minor of
ℓ
G
, or a separation of
G
of order
O
(n
1/2
)
O
(n+m)
O
(n+m)
O
(n
2/3
)
ε∈[0,1/2]
, our algorithm either outputs a
K
-minor of
ℓ
G
, or a separation of
G
with order
O
(n
(2-ε)/3
)
O
(n
1+ε
+m)
|
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| reference: | Bruce Reed and David R. Wood (2005), Fast separation in a graph with an excluded minor , in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 45-50 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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Automatically produced on Di Sep 27 10:09:41 CEST 2005 by gustedt
