| Paper Abstract and Keywords |
| Presentation |
2004-10-15 13:30
[Tutorial Lecture]
Algorithm Aspect of Graph Minor Theory
Ken-ichi Kawarabayashi (Tohoku Univ.) |
| Abstract |
(in Japanese) |
(See Japanese page) |
| (in English) |
We shall survey recent progress on algorithm aspect of graph minor theory.
One of the main results on Graph Minor Project by Robertson and
Seymour is the following.
Given a graph $G$ and $p$ pairs of vertices of $G$ for fixed $p$,
there is a polynomial time (actually $O(n^3)$ algorithm to
decide if there are $p$ mutually disjoint paths of $G$ linking the pair.
If $p$ is part of the input of the problem, then this is one of
Karp's NP-complete problems, and
it remains NP-complete even for planar graphs.
We shall first sketch the algorithm, and explain why
the correctness needs > 500 pages to prove.
Then we shall focus on applications of this result.
Topics include tree-width for planar graphs,
$2$-path problem ($2$-linked graph),
the odd disjoint cycles, the parity paths problems,
Kuratowski's theorem for general surface, nearly-$k$-bipartite
graph problem and algorithm aspect of Hadwiger's conjecture. |
| Keyword |
(in Japanese) |
(See Japanese page) |
| (in English) |
graph minor / disjoint paths / connectivity / Robertson-Seymour / / / / |
| Reference Info. |
IEICE Tech. Rep., vol. 104, no. 339, COMP2004-46, pp. 23-23, Oct. 2004. |
| Paper # |
COMP2004-46 |
| Date of Issue |
2004-10-07 (COMP) |
| ISSN |
Print edition: ISSN 0913-5685 |
| Download PDF |
|
| Conference Information |
| Committee |
COMP |
| Conference Date |
2004-10-14 - 2004-10-15 |
| Place (in Japanese) |
(See Japanese page) |
| Place (in English) |
Tohoku University |
| Topics (in Japanese) |
(See Japanese page) |
| Topics (in English) |
|
| Paper Information |
| Registration To |
COMP |
| Conference Code |
2004-10-COMP |
| Language |
English (Japanese title is available) |
| Title (in Japanese) |
(See Japanese page) |
| Sub Title (in Japanese) |
(See Japanese page) |
| Title (in English) |
Algorithm Aspect of Graph Minor Theory |
| Sub Title (in English) |
|
| Keyword(1) |
graph minor |
| Keyword(2) |
disjoint paths |
| Keyword(3) |
connectivity |
| Keyword(4) |
Robertson-Seymour |
| Keyword(5) |
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| Keyword(6) |
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| Keyword(7) |
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| 1st Author's Name |
Ken-ichi Kawarabayashi |
| 1st Author's Affiliation |
Tohoku University (Tohoku Univ.) |
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| Speaker |
Author-1 |
| Date Time |
2004-10-15 13:30:00 |
| Presentation Time |
60 minutes |
| Registration for |
COMP |
| Paper # |
COMP2004-46 |
| Volume (vol) |
vol.104 |
| Number (no) |
no.339 |
| Page |
p.23 |
| #Pages |
1 |
| Date of Issue |
2004-10-07 (COMP) |
|