On the Excluded Minors for Dyadic Matroids

matroids;matroid representability;excluded minors

Wong, Chung-Yinadvisor:Geelen, Jim ; affiliation1:Faculty of Mathematics ; Geelen, Jim ;

University of Waterloo

关键词: matroids;    Master Thesis;    excluded minors;    matroid representability;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/14367/3/Wong_Chung-Yin.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

The study of the class of dyadic matroids, the matroids representable over both $GF(3)$ and $GF(5)$, is a natural step to finding the excluded minors for $GF(5)$-representability. In this thesis we characterize the ternary matroids $M$ that are excluded minors for dyadic matroids and contains a 3-separation. We will show that one side of the separation has size at most four, and that $M$ is obtained by adding at most four elements to another excluded minor $M'$. This reduces the problem of finding the excluded minors for dyadic matroids to the problem of finding the vertically 4-connected excluded minors for dyadic matroids.