Matching minors in bipartite graphs

Author:: Wiederrecht, Sebastian
Published:: Berlin Universitätsverlag der Technischen Universität Berlin 2022
Physical Description:: 1 electronic resource (476 p.)

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Language Note:

English

Restrictions on Access:

Open Access Unrestricted online access

Summary:

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.

Subject(s):

Algorithms & data structures

Other Subject(s):

matching minor; structural graph theory; bipartite; perfect matching

ISBN:

9783798332522
depositonce-14958

Collection:

OAPEN Library.

Terms of Use and Reproduction:

Creative Commons https://creativecommons.org/licenses/by/4.0/

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