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Description
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 Urbana-Champaign |
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 Urbana-Champaign, 1988. |
URI: | http://hdl.handle.net/2142/71264 |
Other Identifier(s): | (UMI)AAI8815372 |
Date Available in IDEALS: | 2014-12-16 |
Date Deposited: | 1988 |
This item appears in the following Collection(s)
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Dissertations and Theses - Mathematics
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Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois