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Title:  The Total Interval Number of a Graph 
Author(s):  Kratzke, Thomas Martin 
Doctoral Committee Chair(s):  West, Douglas B. 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Mathematics
Computer Science 
Abstract:  An interval representation (or simply representation) R of a graph G is a collection of finite sets $\{R(\nu):\nu \in V(G)\}$ of closed bounded intervals so that $u \leftrightarrow \nu$ if and only if there exist $\theta\sb{u} \in R(u), \theta\sb{\nu} \in R(\nu)$ with $\theta\sb{u} \cap \theta\sb{\nu} \not= \emptyset$. The size of a representation is the number of intervals in the entire collection. The total interval number of G is the size of the smallest representation of G and is denoted I(G). This thesis studies I by proving best possible upper bounds for several classes of graphs. For some classes, the bounds are in terms of n, the number of vertices and for some classes, the bounds are in terms of m, the number of edges. The main result is that for planar graphs, $I(G) \leq 2n(G)  3$. 
Issue Date:  1988 
Type:  Text 
Description:  123 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 1988. 
URI:  http://hdl.handle.net/2142/71264 
Other Identifier(s):  (UMI)AAI8815372 
Date Available in IDEALS:  20141216 
Date Deposited:  1988 
This item appears in the following Collection(s)

Dissertations and Theses  Mathematics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois