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.

ISBN

9780591591286

Pages

97

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