Date of Award
1997
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
First Advisor
Bogdan S. Oporowski
Abstract
In this paper, we study one measure of complexity of a graph, namely its type. The type of a graph G is defined to be the minimum number n such that there is a sequence of graphs $G = G\sb0, G\sb1,\... , G\sb{n},$ where $G\sb{i}$ is obtained by contracting or deleting one edge from each block of $G\sb{i-1}$, and where $G\sb{n}$ is edgeless. We show that a 3-connected graph has large type if and only if it has a minor isomorphic to a large fan. Furthermore, we show that if a graph has large type, then it has a minor isomorphic to a large fan or to a large member of one of two specified families of graphs.
Recommended Citation
Dittmann, John Joseph Jr, "Unavoidable Minors of Graphs of Large Type." (1997). LSU Historical Dissertations and Theses. 6479.
https://repository.lsu.edu/gradschool_disstheses/6479
ISBN
9780591591286
Pages
97
DOI
10.31390/gradschool_disstheses.6479