#### 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://digitalcommons.lsu.edu/gradschool_disstheses/6479

#### ISBN

9780591591286

#### Pages

97