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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 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


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