id |
oapen-20.500.12657-57270
|
record_format |
dspace
|
spelling |
oapen-20.500.12657-572702022-07-09T02:58:53Z Matching minors in bipartite graphs Wiederrecht, Sebastian matching minor; structural graph theory; bipartite; perfect matching bic Book Industry Communication::U Computing & information technology::UM Computer programming / software development::UMB Algorithms & data structures In this thesis we adapt fundamental parts of the Graph Minors series of Robertson and Seymour for the study of matching minors and investigate a connection to the study of directed graphs. We develope matching theoretic to established results of graph minor theory: We characterise the existence of a cross over a conformal cycle by means of a topological property. Furthermore, we develope a theory for perfect matching width, a width parameter for graphs with perfect matchings introduced by Norin. here we show that the disjoint alternating paths problem can be solved in polynomial time on graphs of bounded width. Moreover, we show that every bipartite graph with high perfect matching width must contain a large grid as a matching minor. Finally, we prove an analogue of the we known Flat Wall theorem and provide a qualitative description of all bipartite graphs which exclude a fixed matching minor. 2022-07-08T09:56:49Z 2022-07-08T09:56:49Z 2022 book 9783798332522 https://library.oapen.org/handle/20.500.12657/57270 eng Foundations of computing application/pdf Attribution 4.0 International wiederrecht_sebastian.pdf https://verlag.tu-berlin.de/produkt/978-3-7983-3252-2/ Universitätsverlag der Technischen Universität Berlin 10.14279/depositonce-14958 10.14279/depositonce-14958 e5e3d993-eb32-46aa-8ee9-b5f168659224 9783798332522 16 476 Berlin open access
|
institution |
OAPEN
|
collection |
DSpace
|
language |
English
|
description |
In this thesis we adapt fundamental parts of the Graph Minors series of Robertson and Seymour for the study of matching minors and investigate a connection to the study of directed graphs. We develope matching theoretic to established results of graph minor theory: We characterise the existence of a cross over a conformal cycle by means of a topological property. Furthermore, we develope a theory for perfect matching width, a width parameter for graphs with perfect matchings introduced by Norin. here we show that the disjoint alternating paths problem can be solved in polynomial time on graphs of bounded width. Moreover, we show that every bipartite graph with high perfect matching width must contain a large grid as a matching minor. Finally, we prove an analogue of the we known Flat Wall theorem and provide a qualitative description of all bipartite graphs which exclude a fixed matching minor.
|
title |
wiederrecht_sebastian.pdf
|
spellingShingle |
wiederrecht_sebastian.pdf
|
title_short |
wiederrecht_sebastian.pdf
|
title_full |
wiederrecht_sebastian.pdf
|
title_fullStr |
wiederrecht_sebastian.pdf
|
title_full_unstemmed |
wiederrecht_sebastian.pdf
|
title_sort |
wiederrecht_sebastian.pdf
|
publisher |
Universitätsverlag der Technischen Universität Berlin
|
publishDate |
2022
|
url |
https://verlag.tu-berlin.de/produkt/978-3-7983-3252-2/
|
_version_ |
1771297502055628800
|